Building Blocks for Reliable Complex Nonlinear Numerical Simulations. Chapter 2

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2001-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Numerical Simulations of STOVL Hot Gas Ingestion in Ground Proximity Using a Multigrid Solution Procedure

NASA Technical Reports Server (NTRS)

Wang, Gang

2003-01-01

A multi grid solution procedure for the numerical simulation of turbulent flows in complex geometries has been developed. A Full Multigrid-Full Approximation Scheme (FMG-FAS) is incorporated into the continuity and momentum equations, while the scalars are decoupled from the multi grid V-cycle. A standard kappa-Epsilon turbulence model with wall functions has been used to close the governing equations. The numerical solution is accomplished by solving for the Cartesian velocity components either with a traditional grid staggering arrangement or with a multiple velocity grid staggering arrangement. The two solution methodologies are evaluated for relative computational efficiency. The solution procedure with traditional staggering arrangement is subsequently applied to calculate the flow and temperature fields around a model Short Take-off and Vertical Landing (STOVL) aircraft hovering in ground proximity.

Modeling of Compressible Flow with Friction and Heat Transfer Using the Generalized Fluid System Simulation Program (GFSSP)

NASA Technical Reports Server (NTRS)

Bandyopadhyay, Alak; Majumdar, Alok

2007-01-01

The present paper describes the verification and validation of a quasi one-dimensional pressure based finite volume algorithm, implemented in Generalized Fluid System Simulation Program (GFSSP), for predicting compressible flow with friction, heat transfer and area change. The numerical predictions were compared with two classical solutions of compressible flow, i.e. Fanno and Rayleigh flow. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. On the other hand, Raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Nonuniform grid distribution improves the accuracy of numerical prediction. A benchmark numerical solution of compressible flow in a converging-diverging nozzle with friction and heat transfer has been developed to verify GFSSP's numerical predictions. The numerical predictions compare favorably in all cases.

Numerical simulation of freshwater/seawater interaction in a dual-permeability karst system with conduits: the development of discrete-continuum VDFST-CFP model

NASA Astrophysics Data System (ADS)

Xu, Zexuan; Hu, Bill

2016-04-01

Dual-permeability karst aquifers of porous media and conduit networks with significant different hydrological characteristics are widely distributed in the world. Discrete-continuum numerical models, such as MODFLOW-CFP and CFPv2, have been verified as appropriate approaches to simulate groundwater flow and solute transport in numerical modeling of karst hydrogeology. On the other hand, seawater intrusion associated with fresh groundwater resources contamination has been observed and investigated in numbers of coastal aquifers, especially under conditions of sea level rise. Density-dependent numerical models including SEAWAT are able to quantitatively evaluate the seawater/freshwater interaction processes. A numerical model of variable-density flow and solute transport - conduit flow process (VDFST-CFP) is developed to provide a better description of seawater intrusion and submarine groundwater discharge in a coastal karst aquifer with conduits. The coupling discrete-continuum VDFST-CFP model applies Darcy-Weisbach equation to simulate non-laminar groundwater flow in the conduit system in which is conceptualized and discretized as pipes, while Darcy equation is still used in continuum porous media. Density-dependent groundwater flow and solute transport equations with appropriate density terms in both conduit and porous media systems are derived and numerically solved using standard finite difference method with an implicit iteration procedure. Synthetic horizontal and vertical benchmarks are created to validate the newly developed VDFST-CFP model by comparing with other numerical models such as variable density SEAWAT, couplings of constant density groundwater flow and solute transport MODFLOW/MT3DMS and discrete-continuum CFPv2/UMT3D models. VDFST-CFP model improves the simulation of density dependent seawater/freshwater mixing processes and exchanges between conduit and matrix. Continuum numerical models greatly overestimated the flow rate under turbulent flow condition but discrete-continuum models provide more accurate results. Parameters sensitivities analysis indicates that conduit diameter and friction factor, matrix hydraulic conductivity and porosity are important parameters that significantly affect variable-density flow and solute transport simulation. The pros and cons of model assumptions, conceptual simplifications and numerical techniques in VDFST-CFP are discussed. In general, the development of VDFST-CFP model is an innovation in numerical modeling methodology and could be applied to quantitatively evaluate the seawater/freshwater interaction in coastal karst aquifers. Keywords: Discrete-continuum numerical model; Variable density flow and transport; Coastal karst aquifer; Non-laminar flow

Intercomparison of 3D pore-scale flow and solute transport simulation methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaofan; Mehmani, Yashar; Perkins, William A.

2016-09-01

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include methods that 1) explicitly model the three-dimensional geometry of pore spaces and 2) those that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of class 1, based on direct numerical simulation using computational fluid dynamics (CFD) codes, against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of class 1 based on the immersed-boundary method (IMB),more » lattice Boltzmann method (LBM), smoothed particle hydrodynamics (SPH), as well as a model of class 2 (a pore-network model or PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and nonreactive solute transport, and intercompare the model results with previously reported experimental observations. Experimental observations are limited to measured pore-scale velocities, so solute transport comparisons are made only among the various models. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations).« less

An unconditionally stable method for numerically solving solar sail spacecraft equations of motion

NASA Astrophysics Data System (ADS)

Karwas, Alex

Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach is capable of accurately simulating sailcraft motion. Sailcraft and spacecraft simulations are compared to flight data and to other numerical solution techniques. The new formulation shows an increase in accuracy over a widely used trajectory propagation technique. Simulations for two-dimensional, three-dimensional, and variable attitude trajectories are presented to show the multiple capabilities of the new technique. An element of optimal control is also part of the new technique. An additional equation is added to the sailcraft equations of motion that maximizes thrust in a specific direction. A technical description and results of an example optimization problem are presented. The spacecraft attitude dynamics equations take the simulation a step further by providing control torques using the angular rate and acceleration outputs of the numerical formulation.

Numerical simulation of the transonic flow past the blunted wedge in the diverging channel

NASA Astrophysics Data System (ADS)

Ryabinin, Anatoly

2018-05-01

Positions of shock waves in the 2D channel with a blunted wedge are studied numerically. Solutions of the Euler equations are obtained with finite-volume solver SU2 for 15 variants of channel geometry. Numerical simulations reveal a considerable hysteresis in the shock wave position versus the supersonic Mach number given at the inlet. In the certain range of inlet Mach number, there are asymmetrical solutions of the equations. Small change in the geometry of the channel leads to shift of boundaries of the hysteresis range.

Modeling of multi-band drift in nanowires using a full band Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Hathwar, Raghuraj; Saraniti, Marco; Goodnick, Stephen M.

2016-07-01

We report on a new numerical approach for multi-band drift within the context of full band Monte Carlo (FBMC) simulation and apply this to Si and InAs nanowires. The approach is based on the solution of the Krieger and Iafrate (KI) equations [J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986)], which gives the probability of carriers undergoing interband transitions subject to an applied electric field. The KI equations are based on the solution of the time-dependent Schrödinger equation, and previous solutions of these equations have used Runge-Kutta (RK) methods to numerically solve the KI equations. This approach made the solution of the KI equations numerically expensive and was therefore only applied to a small part of the Brillouin zone (BZ). Here we discuss an alternate approach to the solution of the KI equations using the Magnus expansion (also known as "exponential perturbation theory"). This method is more accurate than the RK method as the solution lies on the exponential map and shares important qualitative properties with the exact solution such as the preservation of the unitary character of the time evolution operator. The solution of the KI equations is then incorporated through a modified FBMC free-flight drift routine and applied throughout the nanowire BZ. The importance of the multi-band drift model is then demonstrated for the case of Si and InAs nanowires by simulating a uniform field FBMC and analyzing the average carrier energies and carrier populations under high electric fields. Numerical simulations show that the average energy of the carriers under high electric field is significantly higher when multi-band drift is taken into consideration, due to the interband transitions allowing carriers to achieve higher energies.

Computer simulation of solutions of polyharmonic equations in plane domain

NASA Astrophysics Data System (ADS)

Kazakova, A. O.

2018-05-01

A systematic study of plane problems of the theory of polyharmonic functions is presented. A method of reducing boundary problems for polyharmonic functions to the system of integral equations on the boundary of the domain is given and a numerical algorithm for simulation of solutions of this system is suggested. Particular attention is paid to the numerical solution of the main tasks when the values of the function and its derivatives are given. Test examples are considered that confirm the effectiveness and accuracy of the suggested algorithm.

Nonisothermal Analysis of Solution Kinetics by Spreadsheet Simulation

ERIC Educational Resources Information Center

de Levie, Robert

2012-01-01

A fast and generally applicable alternative solution to the problem of determining the useful shelf life of medicinal solutions is described. It illustrates the power and convenience of the combination of numerical simulation and nonlinear least squares with a practical pharmaceutical application of chemical kinetics and thermodynamics, validated…

Dynamic Beam Solutions for Real-Time Simulation and Control Development of Flexible Rockets

NASA Technical Reports Server (NTRS)

Su, Weihua; King, Cecilia K.; Clark, Scott R.; Griffin, Edwin D.; Suhey, Jeffrey D.; Wolf, Michael G.

2016-01-01

In this study, flexible rockets are structurally represented by linear beams. Both direct and indirect solutions of beam dynamic equations are sought to facilitate real-time simulation and control development for flexible rockets. The direct solution is completed by numerically integrate the beam structural dynamic equation using an explicit Newmark-based scheme, which allows for stable and fast transient solutions to the dynamics of flexile rockets. Furthermore, in the real-time operation, the bending strain of the beam is measured by fiber optical sensors (FOS) at intermittent locations along the span, while both angular velocity and translational acceleration are measured at a single point by the inertial measurement unit (IMU). Another study in this paper is to find the analytical and numerical solutions of the beam dynamics based on the limited measurement data to facilitate the real-time control development. Numerical studies demonstrate the accuracy of these real-time solutions to the beam dynamics. Such analytical and numerical solutions, when integrated with data processing and control algorithms and mechanisms, have the potential to increase launch availability by processing flight data into the flexible launch vehicle's control system.

Numerical simulations of an elastica pendulum

NASA Astrophysics Data System (ADS)

Sinclair, R.

Folklore would have it that a massless clamped-free elastica undergoing planar motion with a point end mass possesses periodic solutions corresponding to a single mode of oscillation. We present a battery of numerical simulations leading to the single conclusion that these supposed periodic solutions do not exist, due to a strong nonlinear coupling of two modes, the frequency of one of which is apparently inversely proportional to the magnitude of the force acting on the elastica.

Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach.

PubMed

Geng, Xiaolong; Boufadel, Michel C; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L; Miller, Richard S

2014-09-01

A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies. Copyright © 2014 Elsevier B.V. All rights reserved.

Exploring the feasibility of focusing CW light through a scattering medium into closely spaced twin peaks via numerical solutions of Maxwell’s equations

NASA Astrophysics Data System (ADS)

Tseng, Snow H.; Chang, Shih-Hui

2018-04-01

Here we present a numerical simulation to analyze the effect of scattering on focusing light into closely-spaced twin peaks. The pseudospectral time-domain (PSTD) is implemented to model continuous-wave (CW) light propagation through a scattering medium. Simulations show that CW light can propagate through a scattering medium and focus into closely-spaced twin peaks. CW light of various wavelengths focusing into twin peaks with sub-diffraction spacing is simulated. In advance, light propagation through scattering media of various number densities is simulated to decipher the dependence of CW light focusing phenomenon on the scattering medium. The reported simulations demonstrate the feasibility of focusing CW light into twin peaks with sub-diffraction dimensions. More importantly, based upon numerical solutions of Maxwell’s equations, research findings show that the sub-diffraction focusing phenomenon can be achieved with scarce or densely-packed scattering media.

A Level-set based framework for viscous simulation of particle-laden supersonic flows

NASA Astrophysics Data System (ADS)

Das, Pratik; Sen, Oishik; Jacobs, Gustaaf; Udaykumar, H. S.

2017-06-01

Particle-laden supersonic flows are important in natural and industrial processes, such as, volcanic eruptions, explosions, pneumatic conveyance of particle in material processing etc. Numerical study of such high-speed particle laden flows at the mesoscale calls for a numerical framework which allows simulation of supersonic flow around multiple moving solid objects. Only a few efforts have been made toward development of numerical frameworks for viscous simulation of particle-fluid interaction in supersonic flow regime. The current work presents a Cartesian grid based sharp-interface method for viscous simulations of interaction between supersonic flow with moving rigid particles. The no-slip boundary condition is imposed at the solid-fluid interfaces using a modified ghost fluid method (GFM). The current method is validated against the similarity solution of compressible boundary layer over flat-plate and benchmark numerical solution for steady supersonic flow over cylinder. Further validation is carried out against benchmark numerical results for shock induced lift-off of a cylinder in a shock tube. 3D simulation of steady supersonic flow over sphere is performed to compare the numerically obtained drag co-efficient with experimental results. A particle-resolved viscous simulation of shock interaction with a cloud of particles is performed to demonstrate that the current method is suitable for large-scale particle resolved simulations of particle-laden supersonic flows.

Numerical System Solver Developed for the National Cycle Program

NASA Technical Reports Server (NTRS)

Binder, Michael P.

1999-01-01

As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

Numerical solution of 2D-vector tomography problem using the method of approximate inverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna

2016-08-10

We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

Numerical simulations of three-dimensional laminar flow over a backward facing step; flow near side walls

NASA Technical Reports Server (NTRS)

Steinthorsson, Erlendur; Liou, Meng-Sing; Povinelli, Louis A.; Arnone, Andrea

1993-01-01

This paper reports the results of numerical simulations of steady, laminar flow over a backward-facing step. The governing equations used in the simulations are the full 'compressible' Navier-Stokes equations, solutions to which were computed by using a cell-centered, finite volume discretization. The convection terms of the governing equations were discretized by using the Advection Upwind Splitting Method (AUSM), whereas the diffusion terms were discretized using central differencing formulas. The validity and accuracy of the numerical solutions were verified by comparing the results to existing experimental data for flow at identical Reynolds numbers in the same back step geometry. The paper focuses attention on the details of the flow field near the side wall of the geometry.

Simulating the injection of micellar solutions to recover diesel in a sand column.

PubMed

Bernardez, Letícia A; Therrien, René; Lefebvre, René; Martel, Richard

2009-01-26

This paper presents numerical simulations of laboratory experiments where diesel, initially present at 18% residual saturation in a sand column, was recovered by injecting a micellar solution containing the surfactant Hostapur SAS-60 (SAS), and two alcohols, n-butanol (n-BuOH), and n-pentanol (n-PeOH). The micellar solution was developed and optimized for diesel recovery using phase diagrams and soil column experiments. Numerical simulations with the compositional simulator UTCHEM agree with the experimental results and show that the entire residual diesel in the sand column was recovered after the downward injection of 5 pore volumes of the micellar solution. Recovery of diesel occurs by enhanced solubility in the microemulsion phase and by mobilization. An additional series of simulations investigated the effects of phase transfer, alcohol partitioning, and component segregation on diesel recovery. These simulations indicate that diesel can be accurately represented in the model by a single component, but that the pseudo-component approach for active matter and the assumption of local phase equilibrium leads to an underestimation of diesel mobilization.

Simulating the injection of micellar solutions to recover diesel in a sand column

NASA Astrophysics Data System (ADS)

Bernardez, Letícia A.; Therrien, René; Lefebvre, René; Martel, Richard

2009-01-01

This paper presents numerical simulations of laboratory experiments where diesel, initially present at 18% residual saturation in a sand column, was recovered by injecting a micellar solution containing the surfactant Hostapur SAS-60 (SAS), and two alcohols, n-butanol ( n-BuOH), and n-pentanol ( n-PeOH). The micellar solution was developed and optimized for diesel recovery using phase diagrams and soil column experiments. Numerical simulations with the compositional simulator UTCHEM agree with the experimental results and show that the entire residual diesel in the sand column was recovered after the downward injection of 5 pore volumes of the micellar solution. Recovery of diesel occurs by enhanced solubility in the microemulsion phase and by mobilization. An additional series of simulations investigated the effects of phase transfer, alcohol partitioning, and component segregation on diesel recovery. These simulations indicate that diesel can be accurately represented in the model by a single component, but that the pseudo-component approach for active matter and the assumption of local phase equilibrium leads to an underestimation of diesel mobilization.

Guidelines for Computing Longitudinal Dynamic Stability Characteristics of a Subsonic Transport

NASA Technical Reports Server (NTRS)

Thompson, Joseph R.; Frank, Neal T.; Murphy, Patrick C.

2010-01-01

A systematic study is presented to guide the selection of a numerical solution strategy for URANS computation of a subsonic transport configuration undergoing simulated forced oscillation about its pitch axis. Forced oscillation is central to the prevalent wind tunnel methodology for quantifying aircraft dynamic stability derivatives from force and moment coefficients, which is the ultimate goal for the computational simulations. Extensive computations are performed that lead in key insights of the critical numerical parameters affecting solution convergence. A preliminary linear harmonic analysis is included to demonstrate the potential of extracting dynamic stability derivatives from computational solutions.

WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

NASA Astrophysics Data System (ADS)

Crevoisier, David; Voltz, Marc

2013-04-01

To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute fluxes - where Hydrus simulations may fail to converge - no numerical problem appears, and ii) accuracy of simulations even for loose spatial domain discretisations, which can only be obtained by Hydrus with fine discretisations.

Code Verification of the HIGRAD Computational Fluid Dynamics Solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Buren, Kendra L.; Canfield, Jesse M.; Hemez, Francois M.

2012-05-04

The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verificationmore » test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the solver. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the solver performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.« less

Numerical Hydrodynamics in General Relativity.

PubMed

Font, José A

2003-01-01

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them. Supplementary material is available for this article at 10.12942/lrr-2003-4.

A Numerical Simulation of a Normal Sonic Jet into a Hypersonic Cross-Flow

NASA Technical Reports Server (NTRS)

Jeffries, Damon K.; Krishnamurthy, Ramesh; Chandra, Suresh

1997-01-01

This study involves numerical modeling of a normal sonic jet injection into a hypersonic cross-flow. The numerical code used for simulation is GASP (General Aerodynamic Simulation Program.) First the numerical predictions are compared with well established solutions for compressible laminar flow. Then comparisons are made with non-injection test case measurements of surface pressure distributions. Good agreement with the measurements is observed. Currently comparisons are underway with the injection case. All the experimental data were generated at the Southampton University Light Piston Isentropic Compression Tube.

Numerical Simulations of Laminar Air-Water Flow of a Non-linear Progressive Wave at Low Wind Speed

NASA Astrophysics Data System (ADS)

Wen, X.; Mobbs, S.

2014-03-01

A numerical simulation for two-dimensional laminar air-water flow of a non-linear progressive water wave with large steepness is performed when the background wind speed varies from zero to the wave phase speed. It is revealed that in the water the difference between the analytical solution of potential flow and numerical solution of viscous flow is very small, indicating that both solutions of the potential flow and viscous flow describe the water wave very accurately. In the air the solutions of potential and viscous flows are very different due to the effects of viscosity. The velocity distribution in the airflow is strongly influenced by the background wind speed and it is found that three wind speeds, , (the maximum orbital velocity of a water wave), and (the wave phase speed), are important in distinguishing different features of the flow patterns.

Numerical simulation of steady cavitating flow of viscous fluid in a Francis hydroturbine

NASA Astrophysics Data System (ADS)

Panov, L. V.; Chirkov, D. V.; Cherny, S. G.; Pylev, I. M.; Sotnikov, A. A.

2012-09-01

Numerical technique was developed for simulation of cavitating flows through the flow passage of a hydraulic turbine. The technique is based on solution of steady 3D Navier—Stokes equations with a liquid phase transfer equation. The approch for setting boundary conditions meeting the requirements of cavitation testing standard was suggested. Four different models of evaporation and condensation were compared. Numerical simulations for turbines of different specific speed were compared with experiment.

Analytical solutions for coagulation and condensation kinetics of composite particles

NASA Astrophysics Data System (ADS)

Piskunov, Vladimir N.

2013-04-01

The processes of composite particles formation consisting of a mixture of different materials are essential for many practical problems: for analysis of the consequences of accidental releases in atmosphere; for simulation of precipitation formation in clouds; for description of multi-phase processes in chemical reactors and industrial facilities. Computer codes developed for numerical simulation of these processes require optimization of computational methods and verification of numerical programs. Kinetic equations of composite particle formation are given in this work in a concise form (impurity integrated). Coagulation, condensation and external sources associated with nucleation are taken into account. Analytical solutions were obtained in a number of model cases. The general laws for fraction redistribution of impurities were defined. The results can be applied to develop numerical algorithms considerably reducing the simulation effort, as well as to verify the numerical programs for calculation of the formation kinetics of composite particles in the problems of practical importance.

Numerical Aerodynamic Simulation (NAS)

NASA Technical Reports Server (NTRS)

Peterson, V. L.; Ballhaus, W. F., Jr.; Bailey, F. R.

1983-01-01

The history of the Numerical Aerodynamic Simulation Program, which is designed to provide a leading-edge capability to computational aerodynamicists, is traced back to its origin in 1975. Factors motivating its development and examples of solutions to successively refined forms of the governing equations are presented. The NAS Processing System Network and each of its eight subsystems are described in terms of function and initial performance goals. A proposed usage allocation policy is discussed and some initial problems being readied for solution on the NAS system are identified.

Permeability Sensitivity Functions and Rapid Simulation of Hydraulic-Testing Measurements Using Perturbation Theory

NASA Astrophysics Data System (ADS)

Escobar Gómez, J. D.; Torres-Verdín, C.

2018-03-01

Single-well pressure-diffusion simulators enable improved quantitative understanding of hydraulic-testing measurements in the presence of arbitrary spatial variations of rock properties. Simulators of this type implement robust numerical algorithms which are often computationally expensive, thereby making the solution of the forward modeling problem onerous and inefficient. We introduce a time-domain perturbation theory for anisotropic permeable media to efficiently and accurately approximate the transient pressure response of spatially complex aquifers. Although theoretically valid for any spatially dependent rock/fluid property, our single-phase flow study emphasizes arbitrary spatial variations of permeability and anisotropy, which constitute key objectives of hydraulic-testing operations. Contrary to time-honored techniques, the perturbation method invokes pressure-flow deconvolution to compute the background medium's permeability sensitivity function (PSF) with a single numerical simulation run. Subsequently, the first-order term of the perturbed solution is obtained by solving an integral equation that weighs the spatial variations of permeability with the spatial-dependent and time-dependent PSF. Finally, discrete convolution transforms the constant-flow approximation to arbitrary multirate conditions. Multidimensional numerical simulation studies for a wide range of single-well field conditions indicate that perturbed solutions can be computed in less than a few CPU seconds with relative errors in pressure of <5%, corresponding to perturbations in background permeability of up to two orders of magnitude. Our work confirms that the proposed joint perturbation-convolution (JPC) method is an efficient alternative to analytical and numerical solutions for accurate modeling of pressure-diffusion phenomena induced by Neumann or Dirichlet boundary conditions.

Numerical Modeling Tools for the Prediction of Solution Migration Applicable to Mining Site

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martell, M.; Vaughn, P.

1999-01-06

Mining has always had an important influence on cultures and traditions of communities around the globe and throughout history. Today, because mining legislation places heavy emphasis on environmental protection, there is great interest in having a comprehensive understanding of ancient mining and mining sites. Multi-disciplinary approaches (i.e., Pb isotopes as tracers) are being used to explore the distribution of metals in natural environments. Another successful approach is to model solution migration numerically. A proven method to simulate solution migration in natural rock salt has been applied to project through time for 10,000 years the system performance and solution concentrations surroundingmore » a proposed nuclear waste repository. This capability is readily adaptable to simulate solution migration around mining.« less

Monitoring of Batch Industrial Crystallization with Growth, Nucleation, and Agglomeration. Part 1: Modeling with Method of Characteristics.

PubMed

Porru, Marcella; Özkan, Leyla

2017-05-24

This paper develops a new simulation model for crystal size distribution dynamics in industrial batch crystallization. The work is motivated by the necessity of accurate prediction models for online monitoring purposes. The proposed numerical scheme is able to handle growth, nucleation, and agglomeration kinetics by means of the population balance equation and the method of characteristics. The former offers a detailed description of the solid phase evolution, while the latter provides an accurate and efficient numerical solution. In particular, the accuracy of the prediction of the agglomeration kinetics, which cannot be ignored in industrial crystallization, has been assessed by comparing it with solutions in the literature. The efficiency of the solution has been tested on a simulation of a seeded flash cooling batch process. Since the proposed numerical scheme can accurately simulate the system behavior more than hundred times faster than the batch duration, it is suitable for online applications such as process monitoring tools based on state estimators.

Monitoring of Batch Industrial Crystallization with Growth, Nucleation, and Agglomeration. Part 1: Modeling with Method of Characteristics

PubMed Central

2017-01-01

This paper develops a new simulation model for crystal size distribution dynamics in industrial batch crystallization. The work is motivated by the necessity of accurate prediction models for online monitoring purposes. The proposed numerical scheme is able to handle growth, nucleation, and agglomeration kinetics by means of the population balance equation and the method of characteristics. The former offers a detailed description of the solid phase evolution, while the latter provides an accurate and efficient numerical solution. In particular, the accuracy of the prediction of the agglomeration kinetics, which cannot be ignored in industrial crystallization, has been assessed by comparing it with solutions in the literature. The efficiency of the solution has been tested on a simulation of a seeded flash cooling batch process. Since the proposed numerical scheme can accurately simulate the system behavior more than hundred times faster than the batch duration, it is suitable for online applications such as process monitoring tools based on state estimators. PMID:28603342

Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

NASA Astrophysics Data System (ADS)

Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah

2018-04-01

This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual artifact banding phenomenon unlike the proposed method and USRM. In all, the proposed permeability and porosity fields generation coupled with the numerical simulator developed will aid in developing efficient mobility control schemes to improve on poor volumetric sweep efficiency in porous media.

Numerical simulation of crevice corrosion of titanium: Effect of the bold surface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Evitts, R.W.; Postlethwaite, J.; Watson, M.K.

1996-12-01

A rigorous crevice corrosion model has been developed that accounts for the bold metal surfaces exterior to the crevice. The model predicts the time change in concentration of all specified chemical species in the crevice and bulk solution, and has the ability to predict active corrosion. It is applied to the crevice corrosion of a small titanium crevice in both oxygenated and anaerobic sodium chloride solutions. The numerical predictions confirm that oxygen is the driving force for crevice corrosion. During the simulations where oxygen is initially present in both the crevice and bulk solution an acidic chloride solution is developed;more » this is the precursor required for crevice corrosion. The anaerobic case displays no tendency to form such a solution. It is also confirmed that those areas in the crevice that are deoxygenated become anodic and the bold metal surface becomes cathodic. As expected, active corrosion is not attained as the simulations are based on electrochemical and chemical parameters at 25 C.« less

Rotating black hole solutions in relativistic analogue gravity

NASA Astrophysics Data System (ADS)

Giacomelli, Luca; Liberati, Stefano

2017-09-01

Simulation and experimental realization of acoustic black holes in analogue gravity systems have lead to a novel understanding of relevant phenomena such as Hawking radiation or superradiance. We explore here the possibility of using relativistic systems for simulating rotating black hole solutions and possibly get an acoustic analogue of a Kerr black hole. In doing so, we demonstrate a precise relation between nonrelativistic and relativistic solutions and provide a new class of vortex solutions for relativistic systems. Such solutions might be used in the future as a test bed in numerical simulations as well as concrete experiments.

Numerical dissipation vs. subgrid-scale modelling for large eddy simulation

NASA Astrophysics Data System (ADS)

Dairay, Thibault; Lamballais, Eric; Laizet, Sylvain; Vassilicos, John Christos

2017-05-01

This study presents an alternative way to perform large eddy simulation based on a targeted numerical dissipation introduced by the discretization of the viscous term. It is shown that this regularisation technique is equivalent to the use of spectral vanishing viscosity. The flexibility of the method ensures high-order accuracy while controlling the level and spectral features of this purely numerical viscosity. A Pao-like spectral closure based on physical arguments is used to scale this numerical viscosity a priori. It is shown that this way of approaching large eddy simulation is more efficient and accurate than the use of the very popular Smagorinsky model in standard as well as in dynamic version. The main strength of being able to correctly calibrate numerical dissipation is the possibility to regularise the solution at the mesh scale. Thanks to this property, it is shown that the solution can be seen as numerically converged. Conversely, the two versions of the Smagorinsky model are found unable to ensure regularisation while showing a strong sensitivity to numerical errors. The originality of the present approach is that it can be viewed as implicit large eddy simulation, in the sense that the numerical error is the source of artificial dissipation, but also as explicit subgrid-scale modelling, because of the equivalence with spectral viscosity prescribed on a physical basis.

Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Starodumov, Ilya; Kropotin, Nikolai

2016-08-10

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phasemore » Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.« less

Numerical and experimental investigations of dependence of photoacoustic signals from gold nanoparticles on the optical properties

NASA Astrophysics Data System (ADS)

Okawa, Shinpei; Hirasawa, Takeshi; Sato, Ryota; Kushibiki, Toshihiro; Ishihara, Miya; Teranishi, Toshiharu

2018-06-01

Gold nanoparticles (AuNPs) are used as a contrast agent of the photoacoustic (PA) imaging. The efficiency of AuNPs has been discussed with the absorption cross section. However, the effects of the scattering of the light by AuNPs and surrounding medium on the PA signal from AuNPs have not been discussed. The PA signals from the aqueous solution of AuNPs were examined in the numerical simulation and the experiment. In the numerical simulation, the absorption and scattering cross sections of spherical and polyhedral AuNPs were calculated by Mie theory and discrete dipole approximation. Monte Carlo simulation calculated the absorbed light energy in the aqueous solution of AuNPs. Based on the PA wave equation, the PA signals were simulated. In the experiment, the PA signal from the aqueous solution of AuNP was measured by use of a piezoelectric film and a Q-switched Nd:YAG laser operated at 532 nm. The results of the numerical simulation and the experiment agreed well. In the numerical simulation and the experiment, a single Au nanocube with 50-nm edge generated the peak value of the PA signal significantly. It was approximately 350 times and twice as large as the peak values of the spherical AuNPs with 10- and 50-nm diameters, respectively. The peak value of the PA signal depended on both the absorption and scattering coefficients of the AuNPs and the surrounding medium. The peak value increased with the scattering coefficient in a quadratic manner. The character of the temporal profile of the PA signal such as full width at half maximum depended on the scattering coefficient of the AuNPs.

Numerical and experimental investigations of dependence of photoacoustic signals from gold nanoparticles on the optical properties

NASA Astrophysics Data System (ADS)

Okawa, Shinpei; Hirasawa, Takeshi; Sato, Ryota; Kushibiki, Toshihiro; Ishihara, Miya; Teranishi, Toshiharu

2018-04-01

Gold nanoparticles (AuNPs) are used as a contrast agent of the photoacoustic (PA) imaging. The efficiency of AuNPs has been discussed with the absorption cross section. However, the effects of the scattering of the light by AuNPs and surrounding medium on the PA signal from AuNPs have not been discussed. The PA signals from the aqueous solution of AuNPs were examined in the numerical simulation and the experiment. In the numerical simulation, the absorption and scattering cross sections of spherical and polyhedral AuNPs were calculated by Mie theory and discrete dipole approximation. Monte Carlo simulation calculated the absorbed light energy in the aqueous solution of AuNPs. Based on the PA wave equation, the PA signals were simulated. In the experiment, the PA signal from the aqueous solution of AuNP was measured by use of a piezoelectric film and a Q-switched Nd:YAG laser operated at 532 nm. The results of the numerical simulation and the experiment agreed well. In the numerical simulation and the experiment, a single Au nanocube with 50-nm edge generated the peak value of the PA signal significantly. It was approximately 350 times and twice as large as the peak values of the spherical AuNPs with 10- and 50-nm diameters, respectively. The peak value of the PA signal depended on both the absorption and scattering coefficients of the AuNPs and the surrounding medium. The peak value increased with the scattering coefficient in a quadratic manner. The character of the temporal profile of the PA signal such as full width at half maximum depended on the scattering coefficient of the AuNPs.

Numerical investigation of coupled density-driven flow and hydrogeochemical processes below playas

NASA Astrophysics Data System (ADS)

Hamann, Enrico; Post, Vincent; Kohfahl, Claus; Prommer, Henning; Simmons, Craig T.

2015-11-01

Numerical modeling approaches with varying complexity were explored to investigate coupled groundwater flow and geochemical processes in saline basins. Long-term model simulations of a playa system gain insights into the complex feedback mechanisms between density-driven flow and the spatiotemporal patterns of precipitating evaporites and evolving brines. Using a reactive multicomponent transport model approach, the simulations reproduced, for the first time in a numerical study, the evaporite precipitation sequences frequently observed in saline basins ("bull's eyes"). Playa-specific flow, evapoconcentration, and chemical divides were found to be the primary controls for the location of evaporites formed, and the resulting brine chemistry. Comparative simulations with the computationally far less demanding surrogate single-species transport models showed that these were still able to replicate the major flow patterns obtained by the more complex reactive transport simulations. However, the simulated degree of salinization was clearly lower than in reactive multicomponent transport simulations. For example, in the late stages of the simulations, when the brine becomes halite-saturated, the nonreactive simulation overestimated the solute mass by almost 20%. The simulations highlight the importance of the consideration of reactive transport processes for understanding and quantifying geochemical patterns, concentrations of individual dissolved solutes, and evaporite evolution.

Comment on “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition” by A. Aziz, Comm. Nonlinear Sci. Numer. Simul. 2009;14:1064-8

NASA Astrophysics Data System (ADS)

Magyari, Eugen

2011-01-01

In a recent paper published in this Journal the title problem has been investigated numerically. In the present paper the exact solution for the temperature boundary layer is given in terms of the solution of the flow problem (the Blasius problem) in a compact integral form.

Solitary solutions including spatially localized chaos and their interactions in two-dimensional Kolmogorov flow.

PubMed

Hiruta, Yoshiki; Toh, Sadayoshi

2015-12-01

Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.

Modeling of Passive Acoustic Liners from High Fidelity Numerical Simulations

NASA Astrophysics Data System (ADS)

Ferrari, Marcello do Areal Souto

Noise reduction in aviation has been an important focus of study in the last few decades. One common solution is setting up acoustic liners in the internal walls of the engines. However, measurements in the laboratory with liners are expensive and time consuming. The present work proposes a nonlinear physics-based time domain model to predict the acoustic behavior of a given liner in a defined flow condition. The parameters of the model are defined by analysis of accurate numerical solutions of the flow obtained from a high-fidelity numerical code. The length of the cavity is taken into account by using an analytical procedure to account for internal reflections in the interior of the cavity. Vortices and jets originated from internal flow separations are confirmed to be important mechanisms of sound absorption, which defines the overall efficiency of the liner. Numerical simulations at different frequency, geometry and sound pressure level are studied in detail to define the model parameters. Comparisons with high-fidelity numerical simulations show that the proposed model is accurate, robust, and can be used to define a boundary condition simulating a liner in a high-fidelity code.

Numerical simulations of Kadomtsev-Petviashvili soliton interactions

NASA Astrophysics Data System (ADS)

Infeld, E.; Senatorski, A.; Skorupski, A. A.

1995-04-01

The Kadomtsev-Petviashvili equation generalizes that of Korteweg and de Vries to two space dimensions and arises in various weakly dispersive media. Two very different species of soliton solutions are known for one variant, KPI. The first species to be discovered are line solitons, the second are two dimensional lumps. This paper describes numerical simulations, consistent with all constraints of the equation, in which very distorted line solitons break up into smaller line solitons and arrays of lumps. The arrays can interact with one another. In some cases, aspects of the results of the simulations can be understood in the light of specially constructed exact solutions. Simulations in which initial conditions fail to satisfy the constraints of the equation are also described.

Numerical Simulation of the Perrin-Like Experiments

ERIC Educational Resources Information Center

Mazur, Zygmunt; Grech, Dariusz

2008-01-01

A simple model of the random Brownian walk of a spherical mesoscopic particle in viscous liquids is proposed. The model can be solved analytically and simulated numerically. The analytic solution gives the known Einstein-Smoluchowski diffusion law r[superscript 2] = 2Dt, where the diffusion constant D is expressed by the mass and geometry of a…

Spectral-based propagation schemes for time-dependent quantum systems with application to carbon nanotubes

NASA Astrophysics Data System (ADS)

Chen, Zuojing; Polizzi, Eric

2010-11-01

Effective modeling and numerical spectral-based propagation schemes are proposed for addressing the challenges in time-dependent quantum simulations of systems ranging from atoms, molecules, and nanostructures to emerging nanoelectronic devices. While time-dependent Hamiltonian problems can be formally solved by propagating the solutions along tiny simulation time steps, a direct numerical treatment is often considered too computationally demanding. In this paper, however, we propose to go beyond these limitations by introducing high-performance numerical propagation schemes to compute the solution of the time-ordered evolution operator. In addition to the direct Hamiltonian diagonalizations that can be efficiently performed using the new eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a basis-transformed propagation scheme (BTPS) which allow to reduce considerably the simulation times needed by time intervals. It is outlined that BTPS offers the best computational efficiency allowing new perspectives in time-dependent simulations. Finally, these numerical schemes are applied to study the ac response of a (5,5) carbon nanotube within a three-dimensional real-space mesh framework.

Hybrid Particle-Element Simulation of Impact on Composite Orbital Debris Shields

NASA Technical Reports Server (NTRS)

Fahrenthold, Eric P.

2004-01-01

This report describes the development of new numerical methods and new constitutive models for the simulation of hypervelocity impact effects on spacecraft. The research has included parallel implementation of the numerical methods and material models developed under the project. Validation work has included both one dimensional simulations, for comparison with exact solutions, and three dimensional simulations of published hypervelocity impact experiments. The validated formulations have been applied to simulate impact effects in a velocity and kinetic energy regime outside the capabilities of current experimental methods. The research results presented here allow for the expanded use of numerical simulation, as a complement to experimental work, in future design of spacecraft for hypervelocity impact effects.

Spatiotemporal Airy Ince-Gaussian wave packets in strongly nonlocal nonlinear media.

PubMed

Peng, Xi; Zhuang, Jingli; Peng, Yulian; Li, DongDong; Zhang, Liping; Chen, Xingyu; Zhao, Fang; Deng, Dongmei

2018-03-08

The self-accelerating Airy Ince-Gaussian (AiIG) and Airy helical Ince-Gaussian (AihIG) wave packets in strongly nonlocal nonlinear media (SNNM) are obtained by solving the strongly nonlocal nonlinear Schrödinger equation. For the first time, the propagation properties of three dimensional localized AiIG and AihIG breathers and solitons in the SNNM are demonstrated, these spatiotemporal wave packets maintain the self-accelerating and approximately non-dispersion properties in temporal dimension, periodically oscillating (breather state) or steady (soliton state) in spatial dimension. In particular, their numerical experiments of spatial intensity distribution, numerical simulations of spatiotemporal distribution, as well as the transverse energy flow and the angular momentum in SNNM are presented. Typical examples of the obtained solutions are based on the ratio between the input power and the critical power, the ellipticity and the strong nonlocality parameter. The comparisons of analytical solutions with numerical simulations and numerical experiments of the AiIG and AihIG optical solitons show that the numerical results agree well with the analytical solutions in the case of strong nonlocality.

Numerical simulations of the flow with the prescribed displacement of the airfoil and comparison with experiment

NASA Astrophysics Data System (ADS)

Řidký, V.; Šidlof, P.; Vlček, V.

2013-04-01

The work is devoted to comparing measured data with the results of numerical simulations. As mathematical model was used mathematical model whitout turbulence for incompressible flow In the experiment was observed the behavior of designed NACA0015 airfoil in airflow. For the numerical solution was used OpenFOAM computational package, this is open-source software based on finite volume method. In the numerical solution is prescribed displacement of the airfoil, which corresponds to the experiment. The velocity at a point close to the airfoil surface is compared with the experimental data obtained from interferographic measurements of the velocity field. Numerical solution is computed on a 3D mesh composed of about 1 million ortogonal hexahedron elements. The time step is limited by the Courant number. Parallel computations are run on supercomputers of the CIV at Technical University in Prague (HAL and FOX) and on a computer cluster of the Faculty of Mechatronics of Liberec (HYDRA). Run time is fixed at five periods, the results from the fifth periods and average value for all periods are then be compared with experiment.

Numerical Simulation of a Seaway with Breaking

NASA Astrophysics Data System (ADS)

Dommermuth, Douglas; O'Shea, Thomas; Brucker, Kyle; Wyatt, Donald

2012-11-01

The focus of this presentation is to describe the recent efforts to simulate a fully non-linear seaway with breaking by using a high-order spectral (HOS) solution of the free-surface boundary value problem to drive a three-dimensional Volume of Fluid (VOF) solution. Historically, the two main types of simulations to simulate free-surface flows are the boundary integral equations method (BIEM) and high-order spectral (HOS) methods. BIEM calculations fail at the point at which the surface impacts upon itself, if not sooner, and HOS methods can only simulate a single valued free-surface. Both also employ a single-phase approximation in which the effects of the air on the water are neglected. Due to these limitations they are unable to simulate breaking waves and air entrainment. The Volume of Fluid (VOF) method on the other hand is suitable for modeling breaking waves and air entrainment. However it is computationally intractable to generate a realistic non-linear sea-state. Here, we use the HOS solution to quickly drive, or nudge, the VOF solution into a non-linear state. The computational strategies, mathematical formulation, and numerical implementation will be discussed. The results of the VOF simulation of a seaway with breaking will also be presented, and compared to the single phase, single valued HOS results.

On the limits of numerical astronomical solutions used in paleoclimate studies

NASA Astrophysics Data System (ADS)

Zeebe, Richard E.

2017-04-01

Numerical solutions of the equations of the Solar System estimate Earth's orbital parameters in the past and represent the backbone of cyclostratigraphy and astrochronology, now widely applied in geology and paleoclimatology. Given one numerical realization of a Solar System model (i.e., obtained using one code or integrator package), various parameters determine the properties of the solution and usually limit its validity to a certain time period. Such limitations are denoted here as "internal" and include limitations due to (i) the underlying physics/physical model and (ii) numerics. The physics include initial coordinates and velocities of Solar System bodies, treatment of the Moon and asteroids, the Sun's quadrupole moment, and the intrinsic dynamics of the Solar System itself, i.e., its chaotic nature. Numerical issues include solver algorithm, numerical accuracy (e.g., time step), and round-off errors. At present, internal limitations seem to restrict the validity of astronomical solutions to perhaps the past 50 or 60 myr. However, little is currently known about "external" limitations, that is, how do different numerical realizations compare, say, between different investigators using different codes and integrators? Hitherto only two solutions for Earth's eccentricity appear to be used in paleoclimate studies, provided by two different groups that integrated the full Solar System equations over the past >100 myr (Laskar and coworkers and Varadi et al. 2003). In this contribution, I will present results from new Solar System integrations for Earth's eccentricity obtained using the integrator package HNBody (Rauch and Hamilton 2002). I will discuss the various internal limitations listed above within the framework of the present simulations. I will also compare the results to the existing solutions, the details of which are still being sorted out as several simulations are still running at the time of writing.

Numerical Simulations of Multidimensional Flows in Presence of either Strong Shocks or Strong Gravitational Fields

NASA Astrophysics Data System (ADS)

Font, J. A.; Ibanez, J. M.; Marti, J. M.

1993-04-01

Some numerical solutions via local characteristic approach have been obtained describing multidimensional flows. These solutions have been used as tests of a two- dimensional code which extends some high-resolution shock-captunng methods, designed recently to solve nonlinear hyperbolic systems of conservation laws. K words: HYDRODYNAMICS - BLACK HOLE - RELATIVITY - SHOCK WAVES

Global Properties of Fully Convective Accretion Disks from Local Simulations

NASA Astrophysics Data System (ADS)

Bodo, G.; Cattaneo, F.; Mignone, A.; Ponzo, F.; Rossi, P.

2015-08-01

We present an approach to deriving global properties of accretion disks from the knowledge of local solutions derived from numerical simulations based on the shearing box approximation. The approach consists of a two-step procedure. First, a local solution valid for all values of the disk height is constructed by piecing together an interior solution obtained numerically with an analytical exterior radiative solution. The matching is obtained by assuming hydrostatic balance and radiative equilibrium. Although in principle the procedure can be carried out in general, it simplifies considerably when the interior solution is fully convective. In these cases, the construction is analogous to the derivation of the Hayashi tracks for protostars. The second step consists of piecing together the local solutions at different radii to obtain a global solution. Here we use the symmetry of the solutions with respect to the defining dimensionless numbers—in a way similar to the use of homology relations in stellar structure theory—to obtain the scaling properties of the various disk quantities with radius.

Benchmark Problems of the Geothermal Technologies Office Code Comparison Study

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Mark D.; Podgorney, Robert; Kelkar, Sharad M.

A diverse suite of numerical simulators is currently being applied to predict or understand the performance of enhanced geothermal systems (EGS). To build confidence and identify critical development needs for these analytical tools, the United States Department of Energy, Geothermal Technologies Office has sponsored a Code Comparison Study (GTO-CCS), with participants from universities, industry, and national laboratories. A principal objective for the study was to create a community forum for improvement and verification of numerical simulators for EGS modeling. Teams participating in the study were those representing U.S. national laboratories, universities, and industries, and each team brought unique numerical simulationmore » capabilities to bear on the problems. Two classes of problems were developed during the study, benchmark problems and challenge problems. The benchmark problems were structured to test the ability of the collection of numerical simulators to solve various combinations of coupled thermal, hydrologic, geomechanical, and geochemical processes. This class of problems was strictly defined in terms of properties, driving forces, initial conditions, and boundary conditions. Study participants submitted solutions to problems for which their simulation tools were deemed capable or nearly capable. Some participating codes were originally developed for EGS applications whereas some others were designed for different applications but can simulate processes similar to those in EGS. Solution submissions from both were encouraged. In some cases, participants made small incremental changes to their numerical simulation codes to address specific elements of the problem, and in other cases participants submitted solutions with existing simulation tools, acknowledging the limitations of the code. The challenge problems were based on the enhanced geothermal systems research conducted at Fenton Hill, near Los Alamos, New Mexico, between 1974 and 1995. The problems involved two phases of research, stimulation, development, and circulation in two separate reservoirs. The challenge problems had specific questions to be answered via numerical simulation in three topical areas: 1) reservoir creation/stimulation, 2) reactive and passive transport, and 3) thermal recovery. Whereas the benchmark class of problems were designed to test capabilities for modeling coupled processes under strictly specified conditions, the stated objective for the challenge class of problems was to demonstrate what new understanding of the Fenton Hill experiments could be realized via the application of modern numerical simulation tools by recognized expert practitioners.« less

Structural, thermodynamic, and electrical properties of polar fluids and ionic solutions on a hypersphere: Theoretical aspects

NASA Astrophysics Data System (ADS)

Caillol, J. M.

1992-01-01

We generalize previous work [J. Chem. Phys. 94, 597 (1991)] on an alternative to the Ewald method for the numerical simulations of Coulomb fluids. This new method consists in using as a simulation cell the three-dimensional surface of a four-dimensional sphere, or hypersphere. Here, we consider the case of polar fluids and electrolyte solutions. We derive all the formal expressions which are needed for numerical simulations of such systems. It includes a derivation of the multipolar interactions on a hypersphere, the expansion of the pair-correlation functions on rotational invariants, the expression of the static dielectric constant of a polar liquid, the expressions of the frequency-dependent conductivity and dielectric constant of an ionic solution, and the derivation of the Stillinger-Lovett sum rules for conductive systems.

Modeling of turbulent separated flows for aerodynamic applications

NASA Technical Reports Server (NTRS)

Marvin, J. G.

1983-01-01

Steady, high speed, compressible separated flows modeled through numerical simulations resulting from solutions of the mass-averaged Navier-Stokes equations are reviewed. Emphasis is placed on benchmark flows that represent simplified (but realistic) aerodynamic phenomena. These include impinging shock waves, compression corners, glancing shock waves, trailing edge regions, and supersonic high angle of attack flows. A critical assessment of modeling capabilities is provided by comparing the numerical simulations with experiment. The importance of combining experiment, numerical algorithm, grid, and turbulence model to effectively develop this potentially powerful simulation technique is stressed.

Nonlinearity Domination in Hassellmann Equation as a Reason for Alternative Framework of its Numerical Simulation

DTIC Science & Technology

2014-09-30

nonlinear Schrodinger equation. It is well known that dark solitons are exact solutions of such equation. In the present paper it has been shown that gray...Reason for Alternative Framework of its Numerical Simulation Vladimir Zakharov, Andrei Pushkarev Waves and Solitons LLC 1719 W. Marlette Ave...situation; study of the implications of modulational instability on solitons , rogue waves and air-surface interaction. APPROACH Numerical methods

Hypersonic research at Stanford University

NASA Technical Reports Server (NTRS)

Candler, Graham; Maccormack, Robert

1988-01-01

The status of the hypersonic research program at Stanford University is discussed and recent results are highlighted. The main areas of interest in the program are the numerical simulation of radiating, reacting and thermally excited flows, the investigation and numerical solution of hypersonic shock wave physics, the extension of the continuum fluid dynamic equations to the transition regime between continuum and free-molecule flow, and the development of novel numerical algorithms for efficient particulate simulations of flowfields.

The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

1998-01-01

Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently.

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid.

PubMed

Xiao, Li; Luo, Ray

2017-12-07

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

Asymptotic analysis of dissipative waves with applications to their numerical simulation

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1990-01-01

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Development of numerical techniques for simulation of magnetogasdynamics and hypersonic chemistry

NASA Astrophysics Data System (ADS)

Damevin, Henri-Marie

Magnetogasdynamics, the science concerned with the mutual interaction between electromagnetic field and flow of electrically conducting gas, offers promising advances in flow control and propulsion of future hypersonic vehicles. Numerical simulations are essential for understanding phenomena, and for research and development. The current dissertation is devoted to the development and validation of numerical algorithms for the solution of multidimensional magnetogasdynamic equations and the simulation of hypersonic high-temperature effects. Governing equations are derived, based on classical magnetogasdynamic assumptions. Two sets of equations are considered, namely the full equations and equations in the low magnetic Reynolds number approximation. Equations are expressed in a suitable formulation for discretization by finite differences in a computational space. For the full equations, Gauss law for magnetism is enforced using Powell's methodology. The time integration method is a four-stage modified Runge-Kutta scheme, amended with a Total Variation Diminishing model in a postprocessing stage. The eigensystem, required for the Total Variation Diminishing scheme, is derived in generalized three-dimensional coordinate system. For the simulation of hypersonic high-temperature effects, two chemical models are utilized, namely a nonequilibrium model and an equilibrium model. A loosely coupled approach is implemented to communicate between the magnetogasdynamic equations and the chemical models. The nonequilibrium model is a one-temperature, five-species, seventeen-reaction model solved by an implicit flux-vector splitting scheme. The chemical equilibrium model computes thermodynamics properties using curve fit procedures. Selected results are provided, which explore the different features of the numerical algorithms. The shock-capturing properties are validated for shock-tube simulations using numerical solutions reported in the literature. The computations of superfast flows over corners and in convergent channels demonstrate the performances of the algorithm in multiple dimensions. The implementation of diffusion terms is validated by solving the magnetic Rayleigh problem and Hartmann problem, for which analytical solutions are available. Prediction of blunt-body type flow are investigated and compared with numerical solutions reported in the literature. The effectiveness of the chemical models for hypersonic flow over blunt body is examined in various flow conditions. It is shown that the proposed schemes perform well in a variety of test cases, though some limitations have been identified.

Large eddy simulation of incompressible turbulent channel flow

NASA Technical Reports Server (NTRS)

Moin, P.; Reynolds, W. C.; Ferziger, J. H.

1978-01-01

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

Solar Corona Simulation Model With Positivity-preserving Property

NASA Astrophysics Data System (ADS)

Feng, X. S.

2015-12-01

Positivity-preserving is one of crucial problems in solar corona simulation. In such numerical simulation of low plasma β region, keeping density and pressure is a first of all matter to obtain physical sound solution. In the present paper, we utilize the maximum-principle-preserving flux limiting technique to develop a class of second order positivity-preserving Godunov finite volume HLL methods for the solar wind plasma MHD equations. Based on the underlying first order building block of positivity preserving Lax-Friedrichs, our schemes, under the constrained transport (CT) and generalized Lagrange multiplier (GLM) framework, can achieve high order accuracy, a discrete divergence-free condition and positivity of the numerical solution simultaneously without extra CFL constraints. Numerical results in four Carrington rotation during the declining, rising, minimum and maximum solar activity phases are provided to demonstrate the performance of modeling small plasma beta with positivity-preserving property of the proposed method.

Magnetic Field in a Screw Flow with Fluctuations

NASA Astrophysics Data System (ADS)

Titov, V. V.; Stepanov, R. A.; Sokoloff, D. D.

2018-04-01

We consider the influence of fluctuations in a screw flow of a conducting liquid on the effect of magnetic field self-excitation; the solution of this problem is important for experimental realization of a turbulent dynamo. We propose a theoretical approach based on the solution of averaged equations obtained in the limit of a short correlation time. The applicability of this approach is confirmed by direct numerical simulation of the initial equations. We demonstrate the influence of the correlation of fluctuations on the dynamo effect threshold. It is shown that the solution of the mean-field equations differs from the solution based on direct numerical simulation for a finite correlation time. The advantages and disadvantages of the two approaches are estimates, as well as the importance of the discovered difference in the context of problems of magnetic field self-excitation. The influence of helicity and intermittency on the type of the solution is considered.

Numerical schemes for anomalous diffusion of single-phase fluids in porous media

NASA Astrophysics Data System (ADS)

Awotunde, Abeeb A.; Ghanam, Ryad A.; Al-Homidan, Suliman S.; Tatar, Nasser-eddine

2016-10-01

Simulation of fluid flow in porous media is an indispensable part of oil and gas reservoir management. Accurate prediction of reservoir performance and profitability of investment rely on our ability to model the flow behavior of reservoir fluids. Over the years, numerical reservoir simulation models have been based mainly on solutions to the normal diffusion of fluids in the porous reservoir. Recently, however, it has been documented that fluid flow in porous media does not always follow strictly the normal diffusion process. Small deviations from normal diffusion, called anomalous diffusion, have been reported in some experimental studies. Such deviations can be caused by different factors such as the viscous state of the fluid, the fractal nature of the porous media and the pressure pulse in the system. In this work, we present explicit and implicit numerical solutions to the anomalous diffusion of single-phase fluids in heterogeneous reservoirs. An analytical solution is used to validate the numerical solution to the simple homogeneous case. The conventional wellbore flow model is modified to account for anomalous behavior. Example applications are used to show the behavior of wellbore and wellblock pressures during the single-phase anomalous flow of fluids in the reservoirs considered.

A new unconditionally stable and consistent quasi-analytical in-stream water quality solution scheme for CSTR-based water quality simulators

NASA Astrophysics Data System (ADS)

Woldegiorgis, Befekadu Taddesse; van Griensven, Ann; Pereira, Fernando; Bauwens, Willy

2017-06-01

Most common numerical solutions used in CSTR-based in-stream water quality simulators are susceptible to instabilities and/or solution inconsistencies. Usually, they cope with instability problems by adopting computationally expensive small time steps. However, some simulators use fixed computation time steps and hence do not have the flexibility to do so. This paper presents a novel quasi-analytical solution for CSTR-based water quality simulators of an unsteady system. The robustness of the new method is compared with the commonly used fourth-order Runge-Kutta methods, the Euler method and three versions of the SWAT model (SWAT2012, SWAT-TCEQ, and ESWAT). The performance of each method is tested for different hypothetical experiments. Besides the hypothetical data, a real case study is used for comparison. The growth factors we derived as stability measures for the different methods and the R-factor—considered as a consistency measure—turned out to be very useful for determining the most robust method. The new method outperformed all the numerical methods used in the hypothetical comparisons. The application for the Zenne River (Belgium) shows that the new method provides stable and consistent BOD simulations whereas the SWAT2012 model is shown to be unstable for the standard daily computation time step. The new method unconditionally simulates robust solutions. Therefore, it is a reliable scheme for CSTR-based water quality simulators that use first-order reaction formulations.

Quantification of mixing in vesicle suspensions using numerical simulations in two dimensions.

PubMed

Kabacaoğlu, G; Quaife, B; Biros, G

2017-02-01

We study mixing in Stokesian vesicle suspensions in two dimensions on a cylindrical Couette apparatus using numerical simulations. The vesicle flow simulation is done using a boundary integral method, and the advection-diffusion equation for the mixing of the solute is solved using a pseudo-spectral scheme. We study the effect of the area fraction, the viscosity contrast between the inside (the vesicles) and the outside (the bulk) fluid, the initial condition of the solute, and the mixing metric. We compare mixing in the suspension with mixing in the Couette apparatus without vesicles. On the one hand, the presence of vesicles in most cases slightly suppresses mixing. This is because the solute can be only diffused across the vesicle interface and not advected. On the other hand, there exist spatial distributions of the solute for which the unperturbed Couette flow completely fails to mix whereas the presence of vesicles enables mixing. We derive a simple condition that relates the velocity and solute and can be used to characterize the cases in which the presence of vesicles promotes mixing.

Quantification of mixing in vesicle suspensions using numerical simulations in two dimensions

PubMed Central

Quaife, B.; Biros, G.

2017-01-01

We study mixing in Stokesian vesicle suspensions in two dimensions on a cylindrical Couette apparatus using numerical simulations. The vesicle flow simulation is done using a boundary integral method, and the advection-diffusion equation for the mixing of the solute is solved using a pseudo-spectral scheme. We study the effect of the area fraction, the viscosity contrast between the inside (the vesicles) and the outside (the bulk) fluid, the initial condition of the solute, and the mixing metric. We compare mixing in the suspension with mixing in the Couette apparatus without vesicles. On the one hand, the presence of vesicles in most cases slightly suppresses mixing. This is because the solute can be only diffused across the vesicle interface and not advected. On the other hand, there exist spatial distributions of the solute for which the unperturbed Couette flow completely fails to mix whereas the presence of vesicles enables mixing. We derive a simple condition that relates the velocity and solute and can be used to characterize the cases in which the presence of vesicles promotes mixing. PMID:28344432

3D numerical simulation of transient processes in hydraulic turbines

NASA Astrophysics Data System (ADS)

Cherny, S.; Chirkov, D.; Bannikov, D.; Lapin, V.; Skorospelov, V.; Eshkunova, I.; Avdushenko, A.

2010-08-01

An approach for numerical simulation of 3D hydraulic turbine flows in transient operating regimes is presented. The method is based on a coupled solution of incompressible RANS equations, runner rotation equation, and water hammer equations. The issue of setting appropriate boundary conditions is considered in detail. As an illustration, the simulation results for runaway process are presented. The evolution of vortex structure and its effect on computed runaway traces are analyzed.

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

PubMed Central

Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira

2015-01-01

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology. PMID:26356082

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.

2015-01-01

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the isotropic turbulent flow decay, at a relatively high turbulent Mach number, show a nicely behaved spectral decay rate for medium to high wave numbers. The high-order CESE schemes offer very robust solutions even with the presence of strong shocks or widespread shocklets. The explicit formulation in conjunction with a close to unity theoretical upper Courant number bound has the potential to offer an efficient numerical framework for general compressible turbulent flow simulations with unstructured meshes.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

2–stage stochastic Runge–Kutta for stochastic delay differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosli, Norhayati; Jusoh Awang, Rahimah; Bahar, Arifah

2015-05-15

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

Development of solute transport models in YMPYRÄ framework to simulate solute migration in military shooting and training areas

NASA Astrophysics Data System (ADS)

Warsta, L.; Karvonen, T.

2017-12-01

There are currently 25 shooting and training areas in Finland managed by The Finnish Defence Forces (FDF), where military activities can cause contamination of open waters and groundwater reservoirs. In the YMPYRÄ project, a computer software framework is being developed that combines existing open environmental data and proprietary information collected by FDF with computational models to investigate current and prevent future environmental problems. A data centric philosophy is followed in the development of the system, i.e. the models are updated and extended to handle available data from different areas. The results generated by the models are summarized as easily understandable flow and risk maps that can be opened in GIS programs and used in environmental assessments by experts. Substances investigated with the system include explosives and metals such as lead, and both surface and groundwater dominated areas can be simulated. The YMPYRÄ framework is composed of a three dimensional soil and groundwater flow model, several solute transport models and an uncertainty assessment system. Solute transport models in the framework include particle based, stream tube and finite volume based approaches. The models can be used to simulate solute dissolution from source area, transport in the unsaturated layers to groundwater and finally migration in groundwater to water extraction wells and springs. The models can be used to simulate advection, dispersion, equilibrium adsorption on soil particles, solubility and dissolution from solute phase and dendritic solute decay chains. Correct numerical solutions were confirmed by comparing results to analytical 1D and 2D solutions and by comparing the numerical solutions to each other. The particle based and stream tube type solute transport models were useful as they could complement the traditional finite volume based approach which in certain circumstances produced numerical dispersion due to piecewise solution of the governing equations in computational grids and included computationally intensive and in some cases unstable iterative solutions. The YMPYRÄ framework is being developed by WaterHope, Gain Oy, and SITO Oy consulting companies and funded by FDF.

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes.

PubMed

Horno, J; González-Caballero, F; González-Fernández, C F

1990-01-01

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

A numerical model for simulation of bioremediation of hydrocarbons in aquifers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munoz, J.F.; Irarrazaval, M.J.

1998-03-01

A numerical model was developed to describe the bioremediation of hydrocarbons in ground water aquifers considering aerobic degradation. The model solves the independent transport of three solutes (oxygen, hydrocarbons, and microorganisms) in ground water flow using the method of characteristics. Interactions between the three solutes, in which oxygen and hydrocarbons are consumed by microorganisms, are represented by Monod kinetics, solved using a Runge-Kutta method. Model simulations showed good correlation as compared with results of soil column experiments. The model was used to estimate the time needed to remediate the columns, which varied from one to two years.

DIATOM (Data Initialization and Modification) Library Version 7.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crawford, David A.; Schmitt, Robert G.; Hensinger, David M.

DIATOM is a library that provides numerical simulation software with a computational geometry front end that can be used to build up complex problem geometries from collections of simpler shapes. The library provides a parser which allows for application-independent geometry descriptions to be embedded in simulation software input decks. Descriptions take the form of collections of primitive shapes and/or CAD input files and material properties that can be used to describe complex spatial and temporal distributions of numerical quantities (often called “database variables” or “fields”) to help define starting conditions for numerical simulations. The capability is designed to be generalmore » purpose, robust and computationally efficient. By using a combination of computational geometry and recursive divide-and-conquer approximation techniques, a wide range of primitive shapes are supported to arbitrary degrees of fidelity, controllable through user input and limited only by machine resources. Through the use of call-back functions, numerical simulation software can request the value of a field at any time or location in the problem domain. Typically, this is used only for defining initial conditions, but the capability is not limited to just that use. The most recent version of DIATOM provides the ability to import the solution field from one numerical solution as input for another.« less

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

NASA Astrophysics Data System (ADS)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

Documentation for the MODFLOW 6 framework

USGS Publications Warehouse

Hughes, Joseph D.; Langevin, Christian D.; Banta, Edward R.

2017-08-10

MODFLOW is a popular open-source groundwater flow model distributed by the U.S. Geological Survey. Growing interest in surface and groundwater interactions, local refinement with nested and unstructured grids, karst groundwater flow, solute transport, and saltwater intrusion, has led to the development of numerous MODFLOW versions. Often times, there are incompatibilities between these different MODFLOW versions. The report describes a new MODFLOW framework called MODFLOW 6 that is designed to support multiple models and multiple types of models. The framework is written in Fortran using a modular object-oriented design. The primary framework components include the simulation (or main program), Timing Module, Solutions, Models, Exchanges, and Utilities. The first version of the framework focuses on numerical solutions, numerical models, and numerical exchanges. This focus on numerical models allows multiple numerical models to be tightly coupled at the matrix level.

The SCEC/USGS dynamic earthquake rupture code verification exercise

USGS Publications Warehouse

Harris, R.A.; Barall, M.; Archuleta, R.; Dunham, E.; Aagaard, Brad T.; Ampuero, J.-P.; Bhat, H.; Cruz-Atienza, Victor M.; Dalguer, L.; Dawson, P.; Day, S.; Duan, B.; Ely, G.; Kaneko, Y.; Kase, Y.; Lapusta, N.; Liu, Yajing; Ma, S.; Oglesby, D.; Olsen, K.; Pitarka, A.; Song, S.; Templeton, E.

2009-01-01

Numerical simulations of earthquake rupture dynamics are now common, yet it has been difficult to test the validity of these simulations because there have been few field observations and no analytic solutions with which to compare the results. This paper describes the Southern California Earthquake Center/U.S. Geological Survey (SCEC/USGS) Dynamic Earthquake Rupture Code Verification Exercise, where codes that simulate spontaneous rupture dynamics in three dimensions are evaluated and the results produced by these codes are compared using Web-based tools. This is the first time that a broad and rigorous examination of numerous spontaneous rupture codes has been performed—a significant advance in this science. The automated process developed to attain this achievement provides for a future where testing of codes is easily accomplished.Scientists who use computer simulations to understand earthquakes utilize a range of techniques. Most of these assume that earthquakes are caused by slip at depth on faults in the Earth, but hereafter the strategies vary. Among the methods used in earthquake mechanics studies are kinematic approaches and dynamic approaches.The kinematic approach uses a computer code that prescribes the spatial and temporal evolution of slip on the causative fault (or faults). These types of simulations are very helpful, especially since they can be used in seismic data inversions to relate the ground motions recorded in the field to slip on the fault(s) at depth. However, these kinematic solutions generally provide no insight into the physics driving the fault slip or information about why the involved fault(s) slipped that much (or that little). In other words, these kinematic solutions may lack information about the physical dynamics of earthquake rupture that will be most helpful in forecasting future events.To help address this issue, some researchers use computer codes to numerically simulate earthquakes and construct dynamic, spontaneous rupture (hereafter called “spontaneous rupture”) solutions. For these types of numerical simulations, rather than prescribing the slip function at each location on the fault(s), just the friction constitutive properties and initial stress conditions are prescribed. The subsequent stresses and fault slip spontaneously evolve over time as part of the elasto-dynamic solution. Therefore, spontaneous rupture computer simulations of earthquakes allow us to include everything that we know, or think that we know, about earthquake dynamics and to test these ideas against earthquake observations.

Analytical solution and numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe

NASA Astrophysics Data System (ADS)

Cai, Haibing; Xu, Liuxun; Yang, Yugui; Li, Longqi

2018-05-01

Artificial liquid nitrogen freezing technology is widely used in urban underground engineering due to its technical advantages, such as simple freezing system, high freezing speed, low freezing temperature, high strength of frozen soil, and absence of pollution. However, technical difficulties such as undefined range of liquid nitrogen freezing and thickness of frozen wall gradually emerge during the application process. Thus, the analytical solution of the freezing-temperature field of a single pipe is established considering the freezing temperature of soil and the constant temperature of freezing pipe wall. This solution is then applied in a liquid nitrogen freezing project. Calculation results show that the radius of freezing front of liquid nitrogen is proportional to the square root of freezing time. The radius of the freezing front also decreases with decreased the freezing temperature, and the temperature gradient of soil decreases with increased distance from the freezing pipe. The radius of cooling zone in the unfrozen area is approximately four times the radius of the freezing front. Meanwhile, the numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe is conducted using the Abaqus finite-element program. Results show that the numerical simulation of soil temperature distribution law well agrees with the analytical solution, further verifies the reliability of the established analytical solution of the liquid nitrogen freezing-temperature field of a single pipe.

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

DOE PAGES

Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; ...

2015-07-10

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.« less

From the paddle to the beach - A Boussinesq shallow water numerical wave tank based on Madsen and Sørensen's equations

NASA Astrophysics Data System (ADS)

Orszaghova, Jana; Borthwick, Alistair G. L.; Taylor, Paul H.

2012-01-01

This article describes a one-dimensional numerical model of a shallow-water flume with an in-built piston paddle moving boundary wavemaker. The model is based on a set of enhanced Boussinesq equations and the nonlinear shallow water equations. Wave breaking is described approximately, by locally switching to the nonlinear shallow water equations when a critical wave steepness is reached. The moving shoreline is calculated as part of the solution. The piston paddle wavemaker operates on a movable grid, which is Lagrangian on the paddle face and Eulerian away from the paddle. The governing equations are, however, evolved on a fixed mapped grid, and the newly calculated solution is transformed back onto the moving grid via a domain mapping technique. Validation test results are compared against analytical solutions, confirming correct discretisation of the governing equations, wave generation via the numerical paddle, and movement of the wet/dry front. Simulations are presented that reproduce laboratory experiments of wave runup on a plane beach and wave overtopping of a laboratory seawall, involving solitary waves and compact wave groups. In practice, the numerical model is suitable for simulating the propagation of weakly dispersive waves and can additionally model any associated inundation, overtopping or inland flooding within the same simulation.

Numerical simulation for solution of space-time fractional telegraphs equations with local fractional derivatives via HAFSTM

NASA Astrophysics Data System (ADS)

Pandey, Rishi Kumar; Mishra, Hradyesh Kumar

2017-11-01

In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.

Direct numerical simulations of three-dimensional electrokinetic flows

NASA Astrophysics Data System (ADS)

Chiam, Keng-Hwee

2006-11-01

We discuss direct numerical simulations of three-dimensional electrokinetic flows in microfluidic devices. In particular, we focus on the study of the electrokinetic instability that develops when two solutions with different electrical conductivities are coupled to an external electric field. We characterize this ``mixing'' instability as a function of the parameters of the model, namely the Reynolds number of the flow, the electric Peclet number of the electrolyte solution, and the ratio of the electroosmotic to the electroviscous time scales. Finally, we describe how this model breaks down when the length scale of the device approaches the nanoscale, where the width of the electric Debye layer is comparable to the width of the channel, and discuss solutions to overcome this.

Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity.

PubMed

Heitmann, Stewart; Ermentrout, G Bard

2015-06-01

Spatiotemporal waves of synchronized activity are known to arise in oscillatory neural networks with lateral inhibitory coupling. How such patterns respond to dynamic changes in coupling strength is largely unexplored. The present study uses analysis and simulation to investigate the evolution of wave patterns when the strength of lateral inhibition is varied dynamically. Neural synchronization was modeled by a spatial ring of Kuramoto oscillators with Mexican hat lateral coupling. Broad bands of coexisting stable wave solutions were observed at all levels of inhibition. The stability of these waves was formally analyzed in both the infinite ring and the finite ring. The broad range of multi-stability predicted hysteresis in transitions between neighboring wave solutions when inhibition is slowly varied. Numerical simulation confirmed the predicted transitions when inhibition was ramped down from a high initial value. However, non-wave solutions emerged from the uniform solution when inhibition was ramped upward from zero. These solutions correspond to spatially periodic deviations of phase that we call ripple states. Numerical continuation showed that stable ripple states emerge from synchrony via a supercritical pitchfork bifurcation. The normal form of this bifurcation was derived analytically, and its predictions compared against the numerical results. Ripple states were also found to bifurcate from wave solutions, but these were locally unstable. Simulation also confirmed the existence of hysteresis and ripple states in two spatial dimensions. Our findings show that spatial synchronization patterns can remain structurally stable despite substantial changes in network connectivity.

Numerical simulation of wave-induced fluid flow seismic attenuation based on the Cole-Cole model.

PubMed

Picotti, Stefano; Carcione, José M

2017-07-01

The acoustic behavior of porous media can be simulated more realistically using a stress-strain relation based on the Cole-Cole model. In particular, seismic velocity dispersion and attenuation in porous rocks is well described by mesoscopic-loss models. Using the Zener model to simulate wave propagation is a rough approximation, while the Cole-Cole model provides an optimal description of the physics. Here, a time-domain algorithm is proposed based on the Grünwald-Letnikov numerical approximation of the fractional derivative involved in the time-domain representation of the Cole-Cole model, while the spatial derivatives are computed with the Fourier pseudospectral method. The numerical solution is successfully tested against an analytical solution. The methodology is applied to a model of saline aquifer, where carbon dioxide (CO 2 ) is injected. To follow the migration of the gas and detect possible leakages, seismic monitoring surveys should be carried out periodically. To this aim, the sensitivity of the seismic method must be carefully assessed for the specific case. The simulated test considers a possible leakage in the overburden, above the caprock, where the sandstone is partially saturated with gas and brine. The numerical examples illustrate the implementation of the theory.

Efficient field-theoretic simulation of polymer solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Villet, Michael C.; Fredrickson, Glenn H., E-mail: ghf@mrl.ucsb.edu; Department of Materials, University of California, Santa Barbara, California 93106

2014-12-14

We present several developments that facilitate the efficient field-theoretic simulation of polymers by complex Langevin sampling. A regularization scheme using finite Gaussian excluded volume interactions is used to derive a polymer solution model that appears free of ultraviolet divergences and hence is well-suited for lattice-discretized field theoretic simulation. We show that such models can exhibit ultraviolet sensitivity, a numerical pathology that dramatically increases sampling error in the continuum lattice limit, and further show that this pathology can be eliminated by appropriate model reformulation by variable transformation. We present an exponential time differencing algorithm for integrating complex Langevin equations for fieldmore » theoretic simulation, and show that the algorithm exhibits excellent accuracy and stability properties for our regularized polymer model. These developments collectively enable substantially more efficient field-theoretic simulation of polymers, and illustrate the importance of simultaneously addressing analytical and numerical pathologies when implementing such computations.« less

An adaptive time-stepping strategy for solving the phase field crystal model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Zhengru, E-mail: zrzhang@bnu.edu.cn; Ma, Yuan, E-mail: yuner1022@gmail.com; Qiao, Zhonghua, E-mail: zqiao@polyu.edu.hk

2013-09-15

In this work, we will propose an adaptive time step method for simulating the dynamics of the phase field crystal (PFC) model. The numerical simulation of the PFC model needs long time to reach steady state, and then large time-stepping method is necessary. Unconditionally energy stable schemes are used to solve the PFC model. The time steps are adaptively determined based on the time derivative of the corresponding energy. It is found that the use of the proposed time step adaptivity cannot only resolve the steady state solution, but also the dynamical development of the solution efficiently and accurately. Themore » numerical experiments demonstrate that the CPU time is significantly saved for long time simulations.« less

Numerical simulation and growth of Li2Zn2(MoO4)3 single crystals by the top seeded solution growth technique

NASA Astrophysics Data System (ADS)

Sukharev, V.; Sukhanova, E.; Mozhevitina, E.; Sadovsky, A.; Avetissov, I.

2017-06-01

Li2O - ZnO - MoO3 pseudo ternary system was used for the growth of Li2Zn2(MoO4)3 crystals by the top seeded solution growth technique in which MoO3 was used as a solvent. Properties of the melts (density, viscosity) have been experimentally measured at different temperatures and compositions of Li2O - ZnO - MoO3 pseudo ternary system. Heat mass transfer in the crystal growth setup was numerically simulated. Using the simulation results a real growth setup was made, Li2Zn2(MoO4)3 crystals were grown and their properties were studied.

A new theoretical basis for numerical simulations of nonlinear acoustic fields

NASA Astrophysics Data System (ADS)

Wójcik, Janusz

2000-07-01

Nonlinear acoustic equations can be considerably simplified. The presented model retains the accuracy of a more complex description of nonlinearity and a uniform description of near and far fields (in contrast to the KZK equation). A method has been presented for obtaining solutions of Kuznetsov's equation from the solutions of the model under consideration. Results of numerical calculations, including comparative ones, are presented.

You Don't Need Richards'... A New General 1-D Vadose Zone Solution Method that is Reliable

NASA Astrophysics Data System (ADS)

Ogden, F. L.; Lai, W.; Zhu, J.; Steinke, R. C.; Talbot, C. A.

2015-12-01

Hydrologic modelers and mathematicians have strived to improve 1-D Richards' equation (RE) solution reliability for predicting vadose zone fluxes. Despite advances in computing power and the numerical solution of partial differential equations since Richards first published the RE in 1931, the solution remains unreliable. That is to say that there is no guarantee that for a particular set of soil constitutive relations, moisture profile conditions, or forcing input that a numerical RE solver will converge to an answer. This risk of non-convergence renders prohibitive the use of RE solvers in hydrological models that need perhaps millions of infiltration solutions. In lieu of using unreliable numerical RE solutions, researchers have developed a wide array of approximate solutions that more-or-less mimic the behavior of the RE, with some notable deficiencies such as parameter insensitivity or divergence over time. The improved Talbot-Ogden (T-O) finite water-content scheme was shown by Ogden et al. (2015) to be an extremely good approximation of the 1-D RE solution, with a difference in cumulative infiltration of only 0.2 percent over an 8 month simulation comparing the improved T-O scheme with a RE numerical solver. The reason is that the newly-derived fundamental flow equation that underpins the improved T-O method is equivalent to the RE minus a term that is equal to the diffusive flux divided by the slope of the wetting front. Because the diffusive flux has zero mean, this term is not important in calculating the mean flux. The wetting front slope is near infinite (sharp) in coarser soils that produce more significant hydrological interactions between surface and ground waters, which also makes this missing term 1) disappear in the limit, and, 2) create stability challenges for the numerical solution of RE. The improved T-O method is a replacement for the 1-D RE in soils that can be simulated as homogeneous layers, where the user is willing to neglect the effects of soil water diffusivity. This presentation emphasizes the transformative nature of the improved T-O finite water-content solution, and highlights the benefits of the methods' reliability in high-resolution large watershed simulations in the high performance computing environment, and discusses coupling of the soil matrix and non-Darcian macropores.

Analytical solutions for a soil vapor extraction model that incorporates gas phase dispersion and molecular diffusion

NASA Astrophysics Data System (ADS)

Huang, Junqi; Goltz, Mark N.

2017-06-01

To greatly simplify their solution, the equations describing radial advective/dispersive transport to an extraction well in a porous medium typically neglect molecular diffusion. While this simplification is appropriate to simulate transport in the saturated zone, it can result in significant errors when modeling gas phase transport in the vadose zone, as might be applied when simulating a soil vapor extraction (SVE) system to remediate vadose zone contamination. A new analytical solution for the equations describing radial gas phase transport of a sorbing contaminant to an extraction well is presented. The equations model advection, dispersion (including both mechanical dispersion and molecular diffusion), and rate-limited mass transfer of dissolved, separate phase, and sorbed contaminants into the gas phase. The model equations are analytically solved by using the Laplace transform with respect to time. The solutions are represented by confluent hypergeometric functions in the Laplace domain. The Laplace domain solutions are then evaluated using a numerical Laplace inversion algorithm. The solutions can be used to simulate the spatial distribution and the temporal evolution of contaminant concentrations during operation of a soil vapor extraction well. Results of model simulations show that the effect of gas phase molecular diffusion upon concentrations at the extraction well is relatively small, although the effect upon the distribution of concentrations in space is significant. This study provides a tool that can be useful in designing SVE remediation strategies, as well as verifying numerical models used to simulate SVE system performance.

GLOBAL PROPERTIES OF FULLY CONVECTIVE ACCRETION DISKS FROM LOCAL SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bodo, G.; Ponzo, F.; Rossi, P.

2015-08-01

We present an approach to deriving global properties of accretion disks from the knowledge of local solutions derived from numerical simulations based on the shearing box approximation. The approach consists of a two-step procedure. First, a local solution valid for all values of the disk height is constructed by piecing together an interior solution obtained numerically with an analytical exterior radiative solution. The matching is obtained by assuming hydrostatic balance and radiative equilibrium. Although in principle the procedure can be carried out in general, it simplifies considerably when the interior solution is fully convective. In these cases, the construction ismore » analogous to the derivation of the Hayashi tracks for protostars. The second step consists of piecing together the local solutions at different radii to obtain a global solution. Here we use the symmetry of the solutions with respect to the defining dimensionless numbers—in a way similar to the use of homology relations in stellar structure theory—to obtain the scaling properties of the various disk quantities with radius.« less

Numerical simulation of two-phase filtration in the near well bore zone

NASA Astrophysics Data System (ADS)

Maksat, Kalimoldayev; Kalipa, Kuspanova; Kulyash, Baisalbayeva; Orken, Mamyrbayev; Assel, Abdildayeva

2018-04-01

On the basis of the fundamental laws of energy conservation, nonstationary processes of filtration of two-phase liquids in multilayered reservoirs in the near well bore zone are considered. Number of reservoirs, fluid pressure in the given reservoirs, reservoir permeability, oil viscosity, etc. are taken into account upon that. Plane-parallel flow and axisymmetric cases have been studied. In the numerical solution, non-structured meshes are used. Closer to the well, the meshes thicken. The integration step over time is defined by the generalized Courant inequality. As a result, there are no large oscillations in the numerical solutions obtained. Oil production rates, Poisson's ratios, D-diameters of the well, filter height, filter permeability, and cumulative thickness of the filter cake and the area have been taken as the main inputs in numerical simulation of non-stationary processes of two-phase filtration.

Structural, thermodynamic, and electrical properties of polar fluids and ionic solutions on a hypersphere: Results of simulations

NASA Astrophysics Data System (ADS)

Caillol, J. M.; Levesque, D.

1992-01-01

The reliability and the efficiency of a new method suitable for the simulations of dielectric fluids and ionic solutions is established by numerical computations. The efficiency depends on the use of a simulation cell which is the surface of a four-dimensional sphere. The reliability originates from a charge-charge potential solution of the Poisson equation in this confining volume. The computation time, for systems of a few hundred molecules, is reduced by a factor of 2 or 3 compared to this of a simulation performed in a cubic volume with periodic boundary conditions and the Ewald charge-charge potential.

A numerical and experimental study of three-dimensional liquid sloshing in a rotating spherical container

NASA Technical Reports Server (NTRS)

Chen, Kuo-Huey; Kelecy, Franklyn J.; Pletcher, Richard H.

1992-01-01

A numerical and experimental study of three dimensional liquid sloshing inside a partially-filled spherical container undergoing an orbital rotating motion is described. Solutions of the unsteady, three-dimensional Navier-Stokes equations for the case of a gradual spin-up from rest are compared with experimental data obtained using a rotating test rig fitted with two liquid-filled spherical tanks. Data gathered from several experiments are reduced in terms of a dimensionless free surface height for comparison with transient results from the numerical simulations. The numerical solutions are found to compare favorably with the experimental data.

A model for managing sources of groundwater pollution

USGS Publications Warehouse

Gorelick, Steven M.

1982-01-01

The waste disposal capacity of a groundwater system can be maximized while maintaining water quality at specified locations by using a groundwater pollutant source management model that is based upon linear programing and numerical simulation. The decision variables of the management model are solute waste disposal rates at various facilities distributed over space. A concentration response matrix is used in the management model to describe transient solute transport and is developed using the U.S. Geological Survey solute transport simulation model. The management model was applied to a complex hypothetical groundwater system. Large-scale management models were formulated as dual linear programing problems to reduce numerical difficulties and computation time. Linear programing problems were solved using a numerically stable, available code. Optimal solutions to problems with successively longer management time horizons indicated that disposal schedules at some sites are relatively independent of the number of disposal periods. Optimal waste disposal schedules exhibited pulsing rather than constant disposal rates. Sensitivity analysis using parametric linear programing showed that a sharp reduction in total waste disposal potential occurs if disposal rates at any site are increased beyond their optimal values.

On computations of the integrated space shuttle flowfield using overset grids

NASA Technical Reports Server (NTRS)

Chiu, I-T.; Pletcher, R. H.; Steger, J. L.

1990-01-01

Numerical simulations using the thin-layer Navier-Stokes equations and chimera (overset) grid approach were carried out for flows around the integrated space shuttle vehicle over a range of Mach numbers. Body-conforming grids were used for all the component grids. Testcases include a three-component overset grid - the external tank (ET), the solid rocket booster (SRB) and the orbiter (ORB), and a five-component overset grid - the ET, SRB, ORB, forward and aft attach hardware, configurations. The results were compared with the wind tunnel and flight data. In addition, a Poisson solution procedure (a special case of the vorticity-velocity formulation) using primitive variables was developed to solve three-dimensional, irrotational, inviscid flows for single as well as overset grids. The solutions were validated by comparisons with other analytical or numerical solution, and/or experimental results for various geometries. The Poisson solution was also used as an initial guess for the thin-layer Navier-Stokes solution procedure to improve the efficiency of the numerical flow simulations. It was found that this approach resulted in roughly a 30 percent CPU time savings as compared with the procedure solving the thin-layer Navier-Stokes equations from a uniform free stream flowfield.

Physiology driven adaptivity for the numerical solution of the bidomain equations.

PubMed

Whiteley, Jonathan P

2007-09-01

Previous work [Whiteley, J. P. IEEE Trans. Biomed. Eng. 53:2139-2147, 2006] derived a stable, semi-implicit numerical scheme for solving the bidomain equations. This scheme allows the timestep used when solving the bidomain equations numerically to be chosen by accuracy considerations rather than stability considerations. In this study we modify this scheme to allow an adaptive numerical solution in both time and space. The spatial mesh size is determined by the gradient of the transmembrane and extracellular potentials while the timestep is determined by the values of: (i) the fast sodium current; and (ii) the calcium release from junctional sarcoplasmic reticulum to myoplasm current. For two-dimensional simulations presented here, combining the numerical algorithm in the paper cited above with the adaptive algorithm presented here leads to an increase in computational efficiency by a factor of around 250 over previous work, together with significantly less computational memory being required. The speedup for three-dimensional simulations is likely to be more impressive.

Explicit finite-difference simulation of optical integrated devices on massive parallel computers.

PubMed

Sterkenburgh, T; Michels, R M; Dress, P; Franke, H

1997-02-20

An explicit method for the numerical simulation of optical integrated circuits by means of the finite-difference time-domain (FDTD) method is presented. This method, based on an explicit solution of Maxwell's equations, is well established in microwave technology. Although the simulation areas are small, we verified the behavior of three interesting problems, especially nonparaxial problems, with typical aspects of integrated optical devices. Because numerical losses are within acceptable limits, we suggest the use of the FDTD method to achieve promising quantitative simulation results.

Multiple branches of travelling waves for the Gross–Pitaevskii equation

NASA Astrophysics Data System (ADS)

Chiron, David; Scheid, Claire

2018-06-01

Explicit solitary waves are known to exist for the Kadomtsev–Petviashvili-I (KP-I) equation in dimension 2. We first address numerically the question of their Morse index. The results confirm that the lump solitary wave has Morse index one and that the other explicit solutions correspond to excited states. We then turn to the 2D Gross–Pitaevskii (GP) equation, which in some long wave regime converges to the KP-I equation. Numerical simulations have already shown that a branch of travelling waves of GP converges to a ground state of KP-I, expected to be the lump. In this work, we perform numerical simulations showing that other explicit solitary waves solutions to the KP-I equation give rise to new branches of travelling waves of GP corresponding to excited states.

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods

NASA Astrophysics Data System (ADS)

Nguyen, S. T.; Vu, M.-H.; Vu, M. N.; Tang, A. M.

2017-05-01

The present work aims to modeling the thermal conductivity of fractured materials using homogenization-based analytical and pattern-based numerical methods. These materials are considered as a network of cracks distributed inside a solid matrix. Heat flow through such media is perturbed by the crack system. The problem of heat flow across a single crack is firstly investigated. The classical Eshelby's solution, extended to the thermal conduction problem of an ellipsoidal inclusion embedding in an infinite homogeneous matrix, gives an analytical solution of temperature discontinuity across a non-conducting penny-shaped crack. This solution is then validated by the numerical simulation based on the finite elements method. The numerical simulation allows analyzing the effect of crack conductivity. The problem of a single crack is then extended to a medium containing multiple cracks. Analytical estimations for effective thermal conductivity, that take into account the interaction between cracks and their spatial distribution, are developed for the case of non-conducting cracks. Pattern-based numerical method is then employed for both cases non-conducting and conducting cracks. In the case of non-conducting cracks, numerical and analytical methods, both account for the spatial distribution of the cracks, fit perfectly. In the case of conducting cracks, the numerical analyzing of crack conductivity effect shows that highly conducting cracks weakly affect heat flow and the effective thermal conductivity of fractured media.

Dynamical Approach Study of Spurious Numerics in Nonlinear Computations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi (Technical Monitor)

2002-01-01

The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.

Computations of ideal and real gas high altitude plume flows

NASA Technical Reports Server (NTRS)

Feiereisen, William J.; Venkatapathy, Ethiraj

1988-01-01

In the present work, complete flow fields around generic space vehicles in supersonic and hypersonic flight regimes are studied numerically. Numerical simulation is performed with a flux-split, time asymptotic viscous flow solver that incorporates a generalized equilibrium chemistry model. Solutions to generic problems at various altitude and flight conditions show the complexity of the flow, the equilibrium chemical dissociation and its effect on the overall flow field. Viscous ideal gas solutions are compared against equilibrium gas solutions to illustrate the effect of equilibrium chemistry. Improved solution accuracy is achieved through adaptive grid refinement.

An Investigation into Solution Verification for CFD-DEM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fullmer, William D.; Musser, Jordan

This report presents the study of the convergence behavior of the computational fluid dynamicsdiscrete element method (CFD-DEM) method, specifically National Energy Technology Laboratory’s (NETL) open source MFiX code (MFiX-DEM) with a diffusion based particle-tocontinuum filtering scheme. In particular, this study focused on determining if the numerical method had a solution in the high-resolution limit where the grid size is smaller than the particle size. To address this uncertainty, fixed particle beds of two primary configurations were studied: i) fictitious beds where the particles are seeded with a random particle generator, and ii) instantaneous snapshots from a transient simulation of anmore » experimentally relevant problem. Both problems considered a uniform inlet boundary and a pressure outflow. The CFD grid was refined from a few particle diameters down to 1/6 th of a particle diameter. The pressure drop between two vertical elevations, averaged across the bed cross-section was considered as the system response quantity of interest. A least-squares regression method was used to extrapolate the grid-dependent results to an approximate “grid-free” solution in the limit of infinite resolution. The results show that the diffusion based scheme does yield a converging solution. However, the convergence is more complicated than encountered in simpler, single-phase flow problems showing strong oscillations and, at times, oscillations superimposed on top of globally non-monotonic behavior. The challenging convergence behavior highlights the importance of using at least four grid resolutions in solution verification problems so that (over-determined) regression-based extrapolation methods may be applied to approximate the grid-free solution. The grid-free solution is very important in solution verification and VVUQ exercise in general as the difference between it and the reference solution largely determines the numerical uncertainty. By testing different randomized particle configurations of the same general problem (for the fictitious case) or different instances of freezing a transient simulation, the numerical uncertainties appeared to be on the same order of magnitude as ensemble or time averaging uncertainties. By testing different drag laws, almost all cases studied show that model form uncertainty in this one, very important closure relation was larger than the numerical uncertainty, at least with a reasonable CFD grid, roughly five particle diameters. In this study, the diffusion width (filtering length scale) was mostly set at a constant of six particle diameters. A few exploratory tests were performed to show that similar convergence behavior was observed for diffusion widths greater than approximately two particle diameters. However, this subject was not investigated in great detail because determining an appropriate filter size is really a validation question which must be determined by comparison to experimental or highly accurate numerical data. Future studies are being considered targeting solution verification of transient simulations as well as validation of the filter size with direct numerical simulation data.« less

On the efficient and reliable numerical solution of rate-and-state friction problems

NASA Astrophysics Data System (ADS)

Pipping, Elias; Kornhuber, Ralf; Rosenau, Matthias; Oncken, Onno

2016-03-01

We present a mathematically consistent numerical algorithm for the simulation of earthquake rupture with rate-and-state friction. Its main features are adaptive time stepping, a novel algebraic solution algorithm involving nonlinear multigrid and a fixed point iteration for the rate-and-state decoupling. The algorithm is applied to a laboratory scale subduction zone which allows us to compare our simulations with experimental results. Using physical parameters from the experiment, we find a good fit of recurrence time of slip events as well as their rupture width and peak slip. Computations in 3-D confirm efficiency and robustness of our algorithm.

The numerical modelling and process simulation for the fault diagnosis of rotary kiln incinerator.

PubMed

Roh, S D; Kim, S W; Cho, W S

2001-10-01

The numerical modelling and process simulation for the fault diagnosis of rotary kiln incinerator were accomplished. In the numerical modelling, two models applied to the modelling within the kiln are the combustion chamber model including the mass and energy balance equations for two combustion chambers and 3D thermal model. The combustion chamber model predicts temperature within the kiln, flue gas composition, flux and heat of combustion. Using the combustion chamber model and 3D thermal model, the production-rules for the process simulation can be obtained through interrelation analysis between control and operation variables. The process simulation of the kiln is operated with the production-rules for automatic operation. The process simulation aims to provide fundamental solutions to the problems in incineration process by introducing an online expert control system to provide an integrity in process control and management. Knowledge-based expert control systems use symbolic logic and heuristic rules to find solutions for various types of problems. It was implemented to be a hybrid intelligent expert control system by mutually connecting with the process control systems which has the capability of process diagnosis, analysis and control.

Dynamic one-dimensional modeling of secondary settling tanks and system robustness evaluation.

PubMed

Li, Ben; Stenstrom, M K

2014-01-01

One-dimensional secondary settling tank models are widely used in current engineering practice for design and optimization, and usually can be expressed as a nonlinear hyperbolic or nonlinear strongly degenerate parabolic partial differential equation (PDE). Reliable numerical methods are needed to produce approximate solutions that converge to the exact analytical solutions. In this study, we introduced a reliable numerical technique, the Yee-Roe-Davis (YRD) method as the governing PDE solver, and compared its reliability with the prevalent Stenstrom-Vitasovic-Takács (SVT) method by assessing their simulation results at various operating conditions. The YRD method also produced a similar solution to the previously developed Method G and Enquist-Osher method. The YRD and SVT methods were also used for a time-to-failure evaluation, and the results show that the choice of numerical method can greatly impact the solution. Reliable numerical methods, such as the YRD method, are strongly recommended.

Salt-water-freshwater transient upconing - An implicit boundary-element solution

USGS Publications Warehouse

Kemblowski, M.

1985-01-01

The boundary-element method is used to solve the set of partial differential equations describing the flow of salt water and fresh water separated by a sharp interface in the vertical plane. In order to improve the accuracy and stability of the numerical solution, a new implicit scheme was developed for calculating the motion of the interface. The performance of this scheme was tested by means of numerical simulation. The numerical results are compared to experimental results for a salt-water upconing under a drain problem. ?? 1985.

Numerical simulation of dark envelope soliton in plasma

NASA Astrophysics Data System (ADS)

Wang, Fang-Ping; Han, Juan-fang; Zhang, Jie; Gao, Dong-Ning; Li, Zhong-Zheng; Duan, Wen-Shan; Zhang, Heng

2018-03-01

One-dimensional (1-D) particle-in-cell simulation is used to study the propagation of dark envelop solitons described by the nonlinear Schrödinger equation (NLSE) in electron-ion plasmas. The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the dark envelope soliton in plasma. It is demonstrated by our numerical simulation that there is dark envelope soliton in electron-ion plasmas. The numerical results are in good agreements with the analytical ones from the NLSE which is obtained from the reductive perturbation method. The limitation of the amplitude of dark envelop solitons in plasma is noticed.

Quasi-3D Modeling and Efficient Simulation of Laminar Flows in Microfluidic Devices.

PubMed

Islam, Md Zahurul; Tsui, Ying Yin

2016-10-03

A quasi-3D model has been developed to simulate the flow in planar microfluidic systems with low Reynolds numbers. The model was developed by decomposing the flow profile along the height of a microfluidic system into a Fourier series. It was validated against the analytical solution for flow in a straight rectangular channel and the full 3D numerical COMSOL Navier-Stokes solver for flow in a T-channel. Comparable accuracy to the full 3D numerical solution was achieved by using only three Fourier terms with a significant decrease in computation time. The quasi-3D model was used to model flows in a micro-flow cytometer chip on a desktop computer and good agreement between the simulation and the experimental results was found.

Quasi-3D Modeling and Efficient Simulation of Laminar Flows in Microfluidic Devices

PubMed Central

Islam, Md. Zahurul; Tsui, Ying Yin

2016-01-01

A quasi-3D model has been developed to simulate the flow in planar microfluidic systems with low Reynolds numbers. The model was developed by decomposing the flow profile along the height of a microfluidic system into a Fourier series. It was validated against the analytical solution for flow in a straight rectangular channel and the full 3D numerical COMSOL Navier-Stokes solver for flow in a T-channel. Comparable accuracy to the full 3D numerical solution was achieved by using only three Fourier terms with a significant decrease in computation time. The quasi-3D model was used to model flows in a micro-flow cytometer chip on a desktop computer and good agreement between the simulation and the experimental results was found. PMID:27706104

A one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer 3. Numerical methods and comparisons with exact solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gelbard, F.; Fitzgerald, J.W.; Hoppel, W.A.

1998-07-01

We present the theoretical framework and computational methods that were used by {ital Fitzgerald} {ital et al.} [this issue (a), (b)] describing a one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer. The concepts and limitations of modeling spatially varying multicomponent aerosols are elucidated. New numerical sectional techniques are presented for simulating multicomponent aerosol growth, settling, and eddy transport, coupled to time-dependent and spatially varying condensing vapor concentrations. Comparisons are presented with new exact solutions for settling and particle growth by simultaneous dynamic condensation of one vapor and by instantaneous equilibration with a spatially varying secondmore » vapor. {copyright} 1998 American Geophysical Union« less

Numerical modeling of subsurface radioactive solute transport from waste seepage ponds at the Idaho National Engineering Laboratory

USGS Publications Warehouse

Robertson, John B.

1976-01-01

Aqueous chemical and low-level radioactive effluents have been disposed to seepage ponds since 1952 at the Idaho National Engineering Laboratory. The solutions percolate toward the Snake River Plain aquifer (135 m below) through interlayered basalts and unconsolidated sediments and an extensive zone of ground water perched on a sedimentary layer about 40 m beneath the ponds. A three-segment numerical model was developed to simulate the system, including effects of convection, hydrodynamic dispersion, radioactive decay, and adsorption. Simulated hydraulics and solute migration patterns for all segments agree adequately with the available field data. The model can be used to project subsurface distributions of waste solutes under a variety of assumed conditions for the future. Although chloride and tritium reached the aquifer several years ago, the model analysis suggests that the more easily sorbed solutes, such as cesium-137 and strontium-90, would not reach the aquifer in detectable concentrations within 150 years for the conditions assumed. (Woodard-USGS)

Generation of dense plume fingers in saturated-unsaturated homogeneous porous media

NASA Astrophysics Data System (ADS)

Cremer, Clemens J. M.; Graf, Thomas

2015-02-01

Flow under variable-density conditions is widespread, occurring in geothermal reservoirs, at waste disposal sites or due to saltwater intrusion. The migration of dense plumes typically results in the formation of vertical plume fingers which are known to be triggered by material heterogeneity or by variations in source concentration that causes the density variation. Using a numerical groundwater model, six perturbation methods are tested under saturated and unsaturated flow conditions to mimic heterogeneity and concentration variations on the pore scale in order to realistically generate dense fingers. A laboratory-scale sand tank experiment is numerically simulated, and the perturbation methods are evaluated by comparing plume fingers obtained from the laboratory experiment with numerically simulated fingers. Dense plume fingering for saturated flow can best be reproduced with a spatially random, time-constant perturbation of the solute source. For unsaturated flow, a spatially and temporally random noise of solute concentration or a random conductivity field adequately simulate plume fingering.

Solution of AntiSeepage for Mengxi River Based on Numerical Simulation of Unsaturated Seepage

PubMed Central

Ji, Youjun; Zhang, Linzhi; Yue, Jiannan

2014-01-01

Lessening the leakage of surface water can reduce the waste of water resources and ground water pollution. To solve the problem that Mengxi River could not store water enduringly, geology investigation, theoretical analysis, experiment research, and numerical simulation analysis were carried out. Firstly, the seepage mathematical model was established based on unsaturated seepage theory; secondly, the experimental equipment for testing hydraulic conductivity of unsaturated soil was developed to obtain the curve of two-phase flow. The numerical simulation of leakage in natural conditions proves the previous inference and leakage mechanism of river. At last, the seepage control capacities of different impervious materials were compared by numerical simulations. According to the engineering actuality, the impervious material was selected. The impervious measure in this paper has been proved to be effectible by hydrogeological research today. PMID:24707199

Targeted numerical simulations of binary black holes for GW170104

NASA Astrophysics Data System (ADS)

Healy, J.; Lange, J.; O'Shaughnessy, R.; Lousto, C. O.; Campanelli, M.; Williamson, A. R.; Zlochower, Y.; Calderón Bustillo, J.; Clark, J. A.; Evans, C.; Ferguson, D.; Ghonge, S.; Jani, K.; Khamesra, B.; Laguna, P.; Shoemaker, D. M.; Boyle, M.; García, A.; Hemberger, D. A.; Kidder, L. E.; Kumar, P.; Lovelace, G.; Pfeiffer, H. P.; Scheel, M. A.; Teukolsky, S. A.

2018-03-01

In response to LIGO's observation of GW170104, we performed a series of full numerical simulations of binary black holes, each designed to replicate likely realizations of its dynamics and radiation. These simulations have been performed at multiple resolutions and with two independent techniques to solve Einstein's equations. For the nonprecessing and precessing simulations, we demonstrate the two techniques agree mode by mode, at a precision substantially in excess of statistical uncertainties in current LIGO's observations. Conversely, we demonstrate our full numerical solutions contain information which is not accurately captured with the approximate phenomenological models commonly used to infer compact binary parameters. To quantify the impact of these differences on parameter inference for GW170104 specifically, we compare the predictions of our simulations and these approximate models to LIGO's observations of GW170104.

Numerical Simulation of the Freeze-Thaw Behavior of Mortar Containing Deicing Salt Solution

PubMed Central

Esmaeeli, Hadi S.; Farnam, Yaghoob; Bentz, Dale P.; Zavattieri, Pablo D.; Weiss, Jason

2016-01-01

This paper presents a one-dimensional finite difference model that is developed to describe the freeze-thaw behavior of an air-entrained mortar containing deicing salt solution. A phenomenological model is used to predict the temperature and the heat flow for mortar specimens during cooling and heating. Phase transformations associated with the freezing/melting of water/ice or transition of the eutectic solution from liquid to solid are included in this phenomenological model. The lever rule is used to calculate the quantity of solution that undergoes the phase transformation, thereby simulating the energy released/absorbed during phase transformation. Undercooling and pore size effects are considered in the numerical model. To investigate the effect of pore size distribution, this distribution is considered using the Gibbs-Thomson equation in a saturated mortar specimen. For an air-entrained mortar, the impact of considering pore size (and curvature) on freezing was relatively insignificant; however the impact of pore size is much more significant during melting. The fluid inside pores smaller than 5 nm (i.e., gel pores) has a relatively small contribution in the macroscopic freeze-thaw behavior of mortar specimens within the temperature range used in this study (i.e., +24 °C to −35 °C), and can therefore be neglected for the macroscopic freeze-thaw simulations. A heat sink term is utilized to simulate the heat dissipation during phase transformations. Data from experiments performed using a low-temperature longitudinal guarded comparative calorimeter (LGCC) on mortar specimens fully saturated with various concentration NaCl solutions or partially saturated with water is compared to the numerical results and a promising agreement is generally obtained. PMID:28082830

Numerical Simulation of the Freeze-Thaw Behavior of Mortar Containing Deicing Salt Solution.

PubMed

Esmaeeli, Hadi S; Farnam, Yaghoob; Bentz, Dale P; Zavattieri, Pablo D; Weiss, Jason

2017-02-01

This paper presents a one-dimensional finite difference model that is developed to describe the freeze-thaw behavior of an air-entrained mortar containing deicing salt solution. A phenomenological model is used to predict the temperature and the heat flow for mortar specimens during cooling and heating. Phase transformations associated with the freezing/melting of water/ice or transition of the eutectic solution from liquid to solid are included in this phenomenological model. The lever rule is used to calculate the quantity of solution that undergoes the phase transformation, thereby simulating the energy released/absorbed during phase transformation. Undercooling and pore size effects are considered in the numerical model. To investigate the effect of pore size distribution, this distribution is considered using the Gibbs-Thomson equation in a saturated mortar specimen. For an air-entrained mortar, the impact of considering pore size (and curvature) on freezing was relatively insignificant; however the impact of pore size is much more significant during melting. The fluid inside pores smaller than 5 nm (i.e., gel pores) has a relatively small contribution in the macroscopic freeze-thaw behavior of mortar specimens within the temperature range used in this study (i.e., +24 °C to -35 °C), and can therefore be neglected for the macroscopic freeze-thaw simulations. A heat sink term is utilized to simulate the heat dissipation during phase transformations. Data from experiments performed using a low-temperature longitudinal guarded comparative calorimeter (LGCC) on mortar specimens fully saturated with various concentration NaCl solutions or partially saturated with water is compared to the numerical results and a promising agreement is generally obtained.

Transonic Navier-Stokes solutions of three-dimensional afterbody flows

NASA Technical Reports Server (NTRS)

Compton, William B., III; Thomas, James L.; Abeyounis, William K.; Mason, Mary L.

1989-01-01

The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

PubMed

Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo

2016-05-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

PubMed Central

Sun, Hui; Zhou, Shenggao; Moore, David K.; Cheng, Li-Tien; Li, Bo

2015-01-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems. PMID:27365866

Numerical modeling of solute transport in a sand tank physical model under varying hydraulic gradient and hydrological stresses

NASA Astrophysics Data System (ADS)

Atlabachew, Abunu; Shu, Longcang; Wu, Peipeng; Zhang, Yongjie; Xu, Yang

2018-03-01

This laboratory study improves the understanding of the impacts of horizontal hydraulic gradient, artificial recharge, and groundwater pumping on solute transport through aquifers. Nine experiments and numerical simulations were carried out using a sand tank. The variable-density groundwater flow and sodium chloride transport were simulated using the three-dimensional numerical model SEAWAT. Numerical modelling results successfully reproduced heads and concentrations observed in the sand tank. A higher horizontal hydraulic gradient enhanced the migration of sodium chloride, particularly in the groundwater flow direction. The application of constant artificial recharge increased the spread of the sodium chloride plume in both the longitudinal and lateral directions. In addition, groundwater pumping accelerated spreading of the sodium chloride plume towards the pumping well. Both higher hydraulic gradient and pumping rate generated oval-shaped plumes in the horizontal plane. However, the artificial recharge process produced stretched plumes. These effects of artificial recharge and groundwater pumping were greater under higher hydraulic gradient. The concentration breakthrough curves indicated that emerging solutions never attained the concentration of the originally injected solution. This is probably because of sorption of sodium chloride onto the silica sand and/or the exchange of sodium chloride between the mobile and immobile liquid domains. The fingering and protruding plume shapes in the numerical models constitute instability zones produced by buoyancy-driven flow. Overall, the results have substantiated the influences of hydraulic gradient, boundary condition, artificial recharge, pumping rate and density differences on solute transport through a homogeneous unconfined aquifer. The implications of these findings are important for managing liquid wastes.

An Empirical Model-based MOE for Friction Reduction by Slot-Ejected Polymer Solutions in an Aqueous Environment

DTIC Science & Technology

2007-12-21

of hydrodynamics and the physical characteristics of the polymers. The physics models include both analytical models and numerical simulations ...the experimental observations. The numerical simulations also succeed in replicating some experimental measurements. However, there is still no...become quite significant. 4.5 Documentation The complete model is coded in MatLab . In the model, all units are cgs, so distances are in

Tensor-product preconditioners for a space-time discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2014-10-01

A space-time discontinuous Galerkin spectral element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is presented. A diagonalized alternating direction implicit preconditioner is extended to a space-time formulation using entropy variables. The effectiveness of this technique is demonstrated for the direct numerical simulation of turbulent flow in a channel.

A methodology for the rigorous verification of plasma simulation codes

NASA Astrophysics Data System (ADS)

Riva, Fabio

2016-10-01

The methodology used to assess the reliability of numerical simulation codes constitutes the Verification and Validation (V&V) procedure. V&V is composed by two separate tasks: the verification, which is a mathematical issue targeted to assess that the physical model is correctly solved, and the validation, which determines the consistency of the code results, and therefore of the physical model, with experimental data. In the present talk we focus our attention on the verification, which in turn is composed by the code verification, targeted to assess that a physical model is correctly implemented in a simulation code, and the solution verification, that quantifies the numerical error affecting a simulation. Bridging the gap between plasma physics and other scientific domains, we introduced for the first time in our domain a rigorous methodology for the code verification, based on the method of manufactured solutions, as well as a solution verification based on the Richardson extrapolation. This methodology was applied to GBS, a three-dimensional fluid code based on a finite difference scheme, used to investigate the plasma turbulence in basic plasma physics experiments and in the tokamak scrape-off layer. Overcoming the difficulty of dealing with a numerical method intrinsically affected by statistical noise, we have now generalized the rigorous verification methodology to simulation codes based on the particle-in-cell algorithm, which are employed to solve Vlasov equation in the investigation of a number of plasma physics phenomena.

Numerical Hydrodynamics in General Relativity.

PubMed

Font, José A

2000-01-01

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented. Supplementary material is available for this article at 10.12942/lrr-2000-2.

Numerical simulation of two-dimensional heat transfer in composite bodies with application to de-icing of aircraft components. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Chao, D. F. K.

1983-01-01

Transient, numerical simulations of the de-icing of composite aircraft components by electrothermal heating were performed for a two dimensional rectangular geometry. The implicit Crank-Nicolson formulation was used to insure stability of the finite-difference heat conduction equations and the phase change in the ice layer was simulated using the Enthalpy method. The Gauss-Seidel point iterative method was used to solve the system of difference equations. Numerical solutions illustrating de-icer performance for various composite aircraft structures and environmental conditions are presented. Comparisons are made with previous studies. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Solidification of a binary alloy: Finite-element, single-domain simulation and new benchmark solutions

NASA Astrophysics Data System (ADS)

Le Bars, Michael; Worster, M. Grae

2006-07-01

A finite-element simulation of binary alloy solidification based on a single-domain formulation is presented and tested. Resolution of phase change is first checked by comparison with the analytical results of Worster [M.G. Worster, Solidification of an alloy from a cooled boundary, J. Fluid Mech. 167 (1986) 481-501] for purely diffusive solidification. Fluid dynamical processes without phase change are then tested by comparison with previous numerical studies of thermal convection in a pure fluid [G. de Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Numer. Meth. Fluids 3 (1983) 249-264; D.A. Mayne, A.S. Usmani, M. Crapper, h-adaptive finite element solution of high Rayleigh number thermally driven cavity problem, Int. J. Numer. Meth. Heat Fluid Flow 10 (2000) 598-615; D.C. Wan, B.S.V. Patnaik, G.W. Wei, A new benchmark quality solution for the buoyancy driven cavity by discrete singular convolution, Numer. Heat Transf. 40 (2001) 199-228], in a porous medium with a constant porosity [G. Lauriat, V. Prasad, Non-darcian effects on natural convection in a vertical porous enclosure, Int. J. Heat Mass Transf. 32 (1989) 2135-2148; P. Nithiarasu, K.N. Seetharamu, T. Sundararajan, Natural convective heat transfer in an enclosure filled with fluid saturated variable porosity medium, Int. J. Heat Mass Transf. 40 (1997) 3955-3967] and in a mixed liquid-porous medium with a spatially variable porosity [P. Nithiarasu, K.N. Seetharamu, T. Sundararajan, Natural convective heat transfer in an enclosure filled with fluid saturated variable porosity medium, Int. J. Heat Mass Transf. 40 (1997) 3955-3967; N. Zabaras, D. Samanta, A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes, Int. J. Numer. Meth. Eng. 60 (2004) 1103-1138]. Finally, new benchmark solutions for simultaneous flow through both fluid and porous domains and for convective solidification processes are presented, based on the similarity solutions in corner-flow geometries recently obtained by Le Bars and Worster [M. Le Bars, M.G. Worster, Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification, J. Fluid Mech. (in press)]. Good agreement is found for all tests, hence validating our physical and numerical methods. More generally, the computations presented here could now be considered as standard and reliable analytical benchmarks for numerical simulations, specifically and independently testing the different processes underlying binary alloy solidification.

Numerical simulation of the flow about the F-18 HARV at high angle of attack

NASA Technical Reports Server (NTRS)

Murman, Scott M.

1994-01-01

As part of NASA's High Alpha Technology Program, research has been aimed at developing and extending numerical methods to accurately predict the high Reynolds number flow about the NASA F-18 High Alpha Research Vehicle (HARV) at large angles of attack. The HARV aircraft is equipped with a bidirectional thrust vectoring unit which enables stable, controlled flight through 70 deg angle of attack. Currently, high-fidelity numerical solutions for the flow about the HARV have been obtained at alpha = 30 deg, and validated against flight-test data. It is planned to simulate the flow about the HARV through alpha = 60 deg, and obtain solutions of the same quality as those at the lower angles of attack. This report presents the status of work aimed at extending the HARV computations to the extreme angle of attack range.

An efficient technique for the numerical solution of the bidomain equations.

PubMed

Whiteley, Jonathan P

2008-08-01

Computing the numerical solution of the bidomain equations is widely accepted to be a significant computational challenge. In this study we extend a previously published semi-implicit numerical scheme with good stability properties that has been used to solve the bidomain equations (Whiteley, J.P. IEEE Trans. Biomed. Eng. 53:2139-2147, 2006). A new, efficient numerical scheme is developed which utilizes the observation that the only component of the ionic current that must be calculated on a fine spatial mesh and updated frequently is the fast sodium current. Other components of the ionic current may be calculated on a coarser mesh and updated less frequently, and then interpolated onto the finer mesh. Use of this technique to calculate the transmembrane potential and extracellular potential induces very little error in the solution. For the simulations presented in this study an increase in computational efficiency of over two orders of magnitude over standard numerical techniques is obtained.

Symmetry-plane model of 3D Euler flows: Mapping to regular systems and numerical solutions of blowup

NASA Astrophysics Data System (ADS)

Mulungye, Rachel M.; Lucas, Dan; Bustamante, Miguel D.

2014-11-01

We introduce a family of 2D models describing the dynamics on the so-called symmetry plane of the full 3D Euler fluid equations. These models depend on a free real parameter and can be solved analytically. For selected representative values of the free parameter, we apply the method introduced in [M.D. Bustamante, Physica D: Nonlinear Phenom. 240, 1092 (2011)] to map the fluid equations bijectively to globally regular systems. By comparing the analytical solutions with the results of numerical simulations, we establish that the numerical simulations of the mapped regular systems are far more accurate than the numerical simulations of the original systems, at the same spatial resolution and CPU time. In particular, the numerical integrations of the mapped regular systems produce robust estimates for the growth exponent and singularity time of the main blowup quantity (vorticity stretching rate), converging well to the analytically-predicted values even beyond the time at which the flow becomes under-resolved (i.e. the reliability time). In contrast, direct numerical integrations of the original systems develop unstable oscillations near the reliability time. We discuss the reasons for this improvement in accuracy, and explain how to extend the analysis to the full 3D case. Supported under the programme for Research in Third Level Institutions (PRTLI) Cycle 5 and co-funded by the European Regional Development Fund.

Implicitly solving phase appearance and disappearance problems using two-fluid six-equation model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-01-25

Phase appearance and disappearance issue presents serious numerical challenges in two-phase flow simulations using the two-fluid six-equation model. Numerical challenges arise from the singular equation system when one phase is absent, as well as from the discontinuity in the solution space when one phase appears or disappears. In this work, a high-resolution spatial discretization scheme on staggered grids and fully implicit methods were applied for the simulation of two-phase flow problems using the two-fluid six-equation model. A Jacobian-free Newton-Krylov (JFNK) method was used to solve the discretized nonlinear problem. An improved numerical treatment was proposed and proved to be effectivemore » to handle the numerical challenges. The treatment scheme is conceptually simple, easy to implement, and does not require explicit truncations on solutions, which is essential to conserve mass and energy. Various types of phase appearance and disappearance problems relevant to thermal-hydraulics analysis have been investigated, including a sedimentation problem, an oscillating manometer problem, a non-condensable gas injection problem, a single-phase flow with heat addition problem and a subcooled flow boiling problem. Successful simulations of these problems demonstrate the capability and robustness of the proposed numerical methods and numerical treatments. As a result, volume fraction of the absent phase can be calculated effectively as zero.« less

Numerical simulation of incidence and sweep effects on delta wing vortex breakdown

NASA Technical Reports Server (NTRS)

Ekaterinaris, J. A.; Schiff, Lewis B.

1994-01-01

The structure of the vortical flowfield over delta wings at high angles of attack was investigated. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics, including leading-edge separation, secondary separation, and vortex breakdown. Flows over a 75- and a 63-deg sweep delta wing with sharp leading edges were investigated and compared with available experimental data. The effect of variation of circumferential grid resolution grid resolution in the vicinity of the wing leading edge on the accuracy of the solutions was addressed. Furthermore, the effect of turbulence modeling on the solutions was investigated. The effects of variation of angle of attack on the computed vortical flow structure for the 75-deg sweep delta wing were examined. At moderate angles of attack no vortex breakdown was observed. When a critical angle of attack was reached, bubble-type vortex breakdown was found. With further increase in angle of attack, a change from bubble-type breakdown to spiral-type vortex breakdown was predicted by the numerical solution. The effects of variation of sweep angle and freestream Mach number were addressed with the solutions on a 63-deg sweep delta wing.

Aeroacoustic Simulation of Nose Landing Gear on Adaptive Unstructured Grids With FUN3D

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Khorrami, Mehdi R.; Park, Michael A.; Lockard, David P.

2013-01-01

Numerical simulations have been performed for a partially-dressed, cavity-closed nose landing gear configuration that was tested in NASA Langley s closed-wall Basic Aerodynamic Research Tunnel (BART) and in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D, developed at NASA Langley Research center, is used to compute the unsteady flow field for this configuration. Starting with a coarse grid, a series of successively finer grids were generated using the adaptive gridding methodology available in the FUN3D code. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence model is used for these computations. Time-averaged and instantaneous solutions obtained on these grids are compared with the measured data. In general, the correlation with the experimental data improves with grid refinement. A similar trend is observed for sound pressure levels obtained by using these CFD solutions as input to a FfowcsWilliams-Hawkings noise propagation code to compute the farfield noise levels. In general, the numerical solutions obtained on adapted grids compare well with the hand-tuned enriched fine grid solutions and experimental data. In addition, the grid adaption strategy discussed here simplifies the grid generation process, and results in improved computational efficiency of CFD simulations.

Numerical simulation of three dimensional transonic flows

NASA Technical Reports Server (NTRS)

Sahu, Jubaraj; Steger, Joseph L.

1987-01-01

The three-dimensional flow over a projectile has been computed using an implicit, approximately factored, partially flux-split algorithm. A simple composite grid scheme has been developed in which a single grid is partitioned into a series of smaller grids for applications which require an external large memory device such as the SSD of the CRAY X-MP/48, or multitasking. The accuracy and stability of the composite grid scheme has been tested by numerically simulating the flow over an ellipsoid at angle of attack and comparing the solution with a single grid solution. The flowfield over a projectile at M = 0.96 and 4 deg angle-of-attack has been computed using a fine grid, and compared with experiment.

Numerical Modeling of Pot-Hole Subsidence Due to Shallow Underground Coal Mining in Structurally Disturbed Ground

NASA Astrophysics Data System (ADS)

Lokhande, Ritesh D.; Murthy, V. M. S. R.; Singh, K. B.; Verma, Chandan Prasad; Verma, A. K.

2018-04-01

Stability analysis of underground mining is, generally, complex in nature and is difficult to carry out through analytical solutions more so in case of pot-hole subsidence prediction. Thus, application of numerical modeling technique for simulating and finding a solution is preferred. This paper reports the development of a methodology for simulating the pot-hole subsidence using FLAC3D. This study is restricted to geologically disturbed areas where presence of fault was dominating factor for occurrence of pot-hole subsidence. The results demonstrate that the variation in the excavation geometry and properties of immediate roof rocks play a vital role in the occurrence of pot-hole subsidence.

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Benchmarking FEniCS for mantle convection simulations

NASA Astrophysics Data System (ADS)

Vynnytska, L.; Rognes, M. E.; Clark, S. R.

2013-01-01

This paper evaluates the usability of the FEniCS Project for mantle convection simulations by numerical comparison to three established benchmarks. The benchmark problems all concern convection processes in an incompressible fluid induced by temperature or composition variations, and cover three cases: (i) steady-state convection with depth- and temperature-dependent viscosity, (ii) time-dependent convection with constant viscosity and internal heating, and (iii) a Rayleigh-Taylor instability. These problems are modeled by the Stokes equations for the fluid and advection-diffusion equations for the temperature and composition. The FEniCS Project provides a novel platform for the automated solution of differential equations by finite element methods. In particular, it offers a significant flexibility with regard to modeling and numerical discretization choices; we have here used a discontinuous Galerkin method for the numerical solution of the advection-diffusion equations. Our numerical results are in agreement with the benchmarks, and demonstrate the applicability of both the discontinuous Galerkin method and FEniCS for such applications.

Numeric Modified Adomian Decomposition Method for Power System Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimitrovski, Aleksandar D; Simunovic, Srdjan; Pannala, Sreekanth

This paper investigates the applicability of numeric Wazwaz El Sayed modified Adomian Decomposition Method (WES-ADM) for time domain simulation of power systems. WESADM is a numerical method based on a modified Adomian decomposition (ADM) technique. WES-ADM is a numerical approximation method for the solution of nonlinear ordinary differential equations. The non-linear terms in the differential equations are approximated using Adomian polynomials. In this paper WES-ADM is applied to time domain simulations of multimachine power systems. WECC 3-generator, 9-bus system and IEEE 10-generator, 39-bus system have been used to test the applicability of the approach. Several fault scenarios have been tested.more » It has been found that the proposed approach is faster than the trapezoidal method with comparable accuracy.« less

Numerical simulation of solitary waves on deep water with constant vorticity

NASA Astrophysics Data System (ADS)

Dosaev, A. S.; Shishina, M. I.; Troitskaya, Yu I.

2018-01-01

Characteristics of solitary deep water waves on a flow with constant vorticity are investigated by numerical simulation within the framework of fully nonlinear equations of motion (Euler equations) using the method of surface-tracking conformal coordinates. To ensure that solutions observed are stable, soliton formation as a result of disintegration of an initial pulse-like disturbance is modeled. Evidence is obtained that solitary waves with height above a certain threshold are unstable.

Soliton polarization rotation in fiber lasers

NASA Astrophysics Data System (ADS)

Afanasjev, V. V.

1995-02-01

I have found the approximate analytical solution in explicit form for a vector soliton with an arbitrary component ratio. My solution describes the dependence of soliton intensity on polarization angle and also nonlinear polarization rotation. The analytical results agree well with the numerical simulations.

Design and simulation of a cable-pulley-based transmission for artificial ankle joints

NASA Astrophysics Data System (ADS)

Liu, Huaxin; Ceccarelli, Marco; Huang, Qiang

2016-06-01

In this paper, a mechanical transmission based on cable pulley is proposed for human-like actuation in the artificial ankle joints of human-scale. The anatomy articular characteristics of the human ankle is discussed for proper biomimetic inspiration in designing an accurate, efficient, and robust motion control of artificial ankle joint devices. The design procedure is presented through the inclusion of conceptual considerations and design details for an interactive solution of the transmission system. A mechanical design is elaborated for the ankle joint angular with pitch motion. A multi-body dynamic simulation model is elaborated accordingly and evaluated numerically in the ADAMS environment. Results of the numerical simulations are discussed to evaluate the dynamic performance of the proposed design solution and to investigate the feasibility of the proposed design in future applications for humanoid robots.

Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics

NASA Astrophysics Data System (ADS)

d'Aquino, M.; Capuano, F.; Coppola, G.; Serpico, C.; Mayergoyz, I. D.

2018-05-01

Numerical time integration schemes for Landau-Lifshitz magnetization dynamics are considered. Such dynamics preserves the magnetization amplitude and, in the absence of dissipation, also implies the conservation of the free energy. This property is generally lost when time discretization is performed for the numerical solution. In this work, explicit numerical schemes based on Runge-Kutta methods are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q > p. An effective strategy for adaptive time-stepping control is discussed for schemes of this class. Numerical tests against analytical solutions for the simulation of fast precessional dynamics are performed in order to point out the effectiveness of the proposed methods.

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

NASA Astrophysics Data System (ADS)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

Flow and Transport in Highly Heterogeneous Porous Formations: Numerical Experiments Performed Using the Analytic Element Method

NASA Astrophysics Data System (ADS)

Jankovic, I.

2002-05-01

Flow and transport in porous formations are analyzed using numerical simulations. Hydraulic conductivity is treated as a spatial random function characterized by a probability density function and a two-point covariance function. Simulations are performed for a multi-indicator conductivity structure developed by Gedeon Dagan (personal communication). This conductivity structure contains inhomogeneities (inclusions) of elliptical and ellipsoidal geometry that are embedded in a homogeneous background. By varying the distribution of sizes and conductivities of inclusions, any probability density function and two-point covariance may be reproduced. The multi-indicator structure is selected since it yields simple approximate transport solutions (Aldo Fiori, personal communication) and accurate numerical solutions (based on the Analytic Element Method). The dispersion is examined for two conceptual models. Both models are based on the multi-indicator conductivity structure. The first model is designed to examine dispersion in aquifers with continuously varying conductivity. The inclusions in this model cover as much area/volume of the porous formation as possible. The second model is designed for aquifers that contain clay/sand/gravel lenses embedded in otherwise homogeneous background. The dispersion in both aquifer types is simulated numerically. Simulation results are compared to those obtained using simple approximate solutions. In order to infer transport statistics that are representative of an infinite domain using the numerical experiments, the inclusions are placed in a domain that was shaped as a large ellipse (2D) and a large spheroid (3D) that were submerged in an unbounded homogeneous medium. On a large scale, the large body of inclusions behaves like a single large inhomogeneity. The analytic solution for a uniform flow past the single inhomogeneity of such geometry yields uniform velocity inside the domain. The velocity differs from that at infinity and can be used to infer the effective conductivity of the medium. As many as 100,000 inhomogeneities are placed inside the domain for 2D simulations. Simulations in 3D were limited to 50,000 inclusions. A large number of simulations was conducted on a massively parallel supercomputer cluster at the Center for Computational Research, University at Buffalo. Simulations range from mildly heterogeneous formations to highly heterogeneous formations (variance of the logarithm of conductivity equal to 10) and from sparsely populated systems to systems where inhomogeneities cover 95% of the volume. Particles are released and tracked inside the core of constant mean velocity. Following the particle tracking, various medium, flow, and transport statistics are computed. These include: spatial moments of particle positions, probability density function of hydraulic conductivity and each component of velocity, their two-point covariance function in the direction of flow and normal to it, covariance of Lagrangean velocities, and probability density function of travel times to various break-through locations. Following the analytic nature of the flow solution, all the results are presented in dimensionless forms. For example, the dispersion coefficients are made dimensionless with respect to the mean velocity and size of inhomogeneities. Detailed results will be presented and compared to well known first-order results and the results that are based on simple approximate transport solutions of Aldo Fiori.

Aeroacoustic Simulations of a Nose Landing Gear with FUN3D: A Grid Refinement Study

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Khorrami, Mehdi R.; Lockard, David P.

2017-01-01

A systematic grid refinement study is presented for numerical simulations of a partially-dressed, cavity-closed (PDCC) nose landing gear configuration that was tested in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D is used to compute the unsteady flow field for this configuration. Mixed-element grids generated using the Pointwise (Registered Trademark) grid generation software are used for numerical simulations. Particular care is taken to ensure quality cells and proper resolution in critical areas of interest in an effort to minimize errors introduced by numerical artifacts. A set of grids was generated in this manner to create a family of uniformly refined grids. The finest grid was then modified to coarsen the wall-normal spacing to create a grid suitable for the wall-function implementation in FUN3D code. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence modeling approach is used for these simulations. Time-averaged and instantaneous solutions obtained on these grids are compared with the measured data. These CFD solutions are used as input to a FfowcsWilliams-Hawkings (FW-H) noise propagation code to compute the farfield noise levels. The agreement of the computed results with the experimental data improves as the grid is refined.

An efficient and guaranteed stable numerical method for continuous modeling of infiltration and redistribution with a shallow dynamic water table

NASA Astrophysics Data System (ADS)

Lai, Wencong; Ogden, Fred L.; Steinke, Robert C.; Talbot, Cary A.

2015-03-01

We have developed a one-dimensional numerical method to simulate infiltration and redistribution in the presence of a shallow dynamic water table. This method builds upon the Green-Ampt infiltration with Redistribution (GAR) model and incorporates features from the Talbot-Ogden (T-O) infiltration and redistribution method in a discretized moisture content domain. The redistribution scheme is more physically meaningful than the capillary weighted redistribution scheme in the T-O method. Groundwater dynamics are considered in this new method instead of hydrostatic groundwater front. It is also computationally more efficient than the T-O method. Motion of water in the vadose zone due to infiltration, redistribution, and interactions with capillary groundwater are described by ordinary differential equations. Numerical solutions to these equations are computationally less expensive than solutions of the highly nonlinear Richards' (1931) partial differential equation. We present results from numerical tests on 11 soil types using multiple rain pulses with different boundary conditions, with and without a shallow water table and compare against the numerical solution of Richards' equation (RE). Results from the new method are in satisfactory agreement with RE solutions in term of ponding time, deponding time, infiltration rate, and cumulative infiltrated depth. The new method, which we call "GARTO" can be used as an alternative to the RE for 1-D coupled surface and groundwater models in general situations with homogeneous soils with dynamic water table. The GARTO method represents a significant advance in simulating groundwater surface water interactions because it very closely matches the RE solution while being computationally efficient, with guaranteed mass conservation, and no stability limitations that can affect RE solvers in the case of a near-surface water table.

Validation of a numerical method for interface-resolving simulation of multicomponent gas-liquid mass transfer and evaluation of multicomponent diffusion models

NASA Astrophysics Data System (ADS)

Woo, Mino; Wörner, Martin; Tischer, Steffen; Deutschmann, Olaf

2018-03-01

The multicomponent model and the effective diffusivity model are well established diffusion models for numerical simulation of single-phase flows consisting of several components but are seldom used for two-phase flows so far. In this paper, a specific numerical model for interfacial mass transfer by means of a continuous single-field concentration formulation is combined with the multicomponent model and effective diffusivity model and is validated for multicomponent mass transfer. For this purpose, several test cases for one-dimensional physical or reactive mass transfer of ternary mixtures are considered. The numerical results are compared with analytical or numerical solutions of the Maxell-Stefan equations and/or experimental data. The composition-dependent elements of the diffusivity matrix of the multicomponent and effective diffusivity model are found to substantially differ for non-dilute conditions. The species mole fraction or concentration profiles computed with both diffusion models are, however, for all test cases very similar and in good agreement with the analytical/numerical solutions or measurements. For practical computations, the effective diffusivity model is recommended due to its simplicity and lower computational costs.

Numerical simulation of fire vortex

NASA Astrophysics Data System (ADS)

Barannikova, D. D.; Borzykh, V. E.; Obukhov, A. G.

2018-05-01

The article considers the numerical simulation of the swirling flow of air around the smoothly heated vertical cylindrical domain in the conditions of gravity and Coriolis forces action. The solutions of the complete system of Navie-Stocks equations are numerically solved at constant viscosity and heat conductivity factors. Along with the proposed initial and boundary conditions, these solutions describe the complex non-stationary 3D flows of viscous compressible heat conducting gas. For various instants of time of the initial flow formation stage using the explicit finite-difference scheme the calculations of all gas dynamics parameters, that is density, temperature, pressure and three velocity components of gas particles, have been run. The current instant lines corresponding to the trajectories of the particles movement in the emerging flow have been constructed. A negative direction of the air flow swirling occurred in the vertical cylindrical domain heating has been defined.

Flow in curved ducts of varying cross-section

NASA Astrophysics Data System (ADS)

Sotiropoulos, F.; Patel, V. C.

1992-07-01

Two numerical methods for solving the incompressible Navier-Stokes equations are compared with each other by applying them to calculate laminar and turbulent flows through curved ducts of regular cross-section. Detailed comparisons, between the computed solutions and experimental data, are carried out in order to validate the two methods and to identify their relative merits and disadvantages. Based on the conclusions of this comparative study a numerical method is developed for simulating viscous flows through curved ducts of varying cross-sections. The proposed method is capable of simulating the near-wall turbulence using fine computational meshes across the sublayer in conjunction with a two-layer k-epsilon model. Numerical solutions are obtained for: (1) a straight transition duct geometry, and (2) a hydroturbine draft-tube configuration at model scale Reynolds number for various inlet swirl intensities. The report also provides a detailed literature survey that summarizes all the experimental and computational work in the area of duct flows.

Numerical Hydrodynamics in Special Relativity.

PubMed

Martí, José Maria; Müller, Ewald

2003-01-01

This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction. Supplementary material is available for this article at 10.12942/lrr-2003-7 and is accessible for authorized users.

CURVILINEAR FINITE ELEMENT MODEL FOR SIMULATING TWO-WELL TRACER TESTS AND TRANSPORT IN STRATIFIED AQUIFERS

EPA Science Inventory

The problem of solute transport in steady nonuniform flow created by a recharging and discharging well pair is investigated. Numerical difficulties encountered with the standard Galerkin formulations in Cartesian coordinates are illustrated. An improved finite element solution st...

Analytical and numerical simulation of the steady-state hydrologic effects of mining aggregate in hypothetical sand-and-gravel and fractured crystalline-rock aquifers

USGS Publications Warehouse

Arnold, L.R.; Langer, William H.; Paschke, Suzanne Smith

2003-01-01

Analytical solutions and numerical models were used to predict the extent of steady-state drawdown caused by mining of aggregate below the water table in hypothetical sand-and-gravel and fractured crystalline-rock aquifers representative of hydrogeologic settings in the Front Range area of Colorado. Analytical solutions were used to predict the extent of drawdown under a wide range of hydrologic and mining conditions that assume aquifer homogeneity, isotropy, and infinite extent. Numerical ground-water flow models were used to estimate the extent of drawdown under conditions that consider heterogeneity, anisotropy, and hydrologic boundaries and to simulate complex or unusual conditions not readily simulated using analytical solutions. Analytical simulations indicated that the drawdown radius (or distance) of influence increased as horizontal hydraulic conductivity of the aquifer, mine penetration of the water table, and mine radius increased; radius of influence decreased as aquifer recharge increased. Sensitivity analysis of analytical simulations under intermediate conditions in sand-and-gravel and fractured crystalline-rock aquifers indicated that the drawdown radius of influence was most sensitive to mine penetration of the water table and least sensitive to mine radius. Radius of influence was equally sensitive to changes in horizontal hydraulic conductivity and recharge. Numerical simulations of pits in sand-and- gravel aquifers indicated that the area of influence in a vertically anisotropic sand-and-gravel aquifer of medium size was nearly identical to that in an isotropic aquifer of the same size. Simulated area of influence increased as aquifer size increased and aquifer boundaries were farther away from the pit, and simulated drawdown was greater near the pit when aquifer boundaries were close to the pit. Pits simulated as lined with slurry walls caused mounding to occur upgradient from the pits and drawdown to occur downgradient from the pits. Pits simulated as refilled with water and undergoing evaporative losses had little hydro- logic effect on the aquifer. Numerical sensitivity analyses for simulations of pits in sand-and-gravel aquifers indicated that simulated head was most sensitive to horizontal hydraulic conductivity and the hydraulic conductance of general-head boundaries in the models. Simulated head was less sensitive to riverbed conductance and recharge and relatively insensitive to vertical hydraulic conductivity. Numerical simulations of quarries in fractured crystalline-rock aquifers indicated that the area of influence in a horizontally anisotropic aquifer was elongated in the direction of higher horizontal hydraulic conductivity and shortened in the direction of lower horizontal hydraulic conductivity compared to area of influence in a homogeneous, isotropic aquifer. Area of influence was larger in an aquifer with ground-water flow in deep, low-permeability fractures than in a homogeneous, isotropic aquifer. Area of influence was larger for a quarry intersected by a hydraulically conductive fault zone and smaller for a quarry intersected by a low-conductivity fault zone. Numerical sensitivity analyses for simulations of quarries in fractured crystalline-rock aquifers indicated simulated head was most sensitive to variations in recharge and horizontal hydraulic conductivity, had little sensitivity to vertical hydraulic conductivity and drain cells used to simulate valleys, and was relatively insensitive to drain cells used to simulate the quarry.

Numerical simulation of time delay interferometry for a LISA-like mission with the simplification of having only one interferometer

NASA Astrophysics Data System (ADS)

Dhurandhar, S. V.; Ni, W.-T.; Wang, G.

2013-01-01

In order to attain the requisite sensitivity for LISA, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. In a previous paper (Dhurandhar, S.V., Nayak, K.R., Vinet, J.-Y. Time delay interferometry for LISA with one arm dysfunctional. Class. Quantum Grav. 27, 135013, 2010), we have found a large family of second-generation analytic solutions of time delay interferometry with one arm dysfunctional, and we also estimated the laser noise due to residual time-delay semi-analytically from orbit perturbations due to Earth. Since other planets and solar-system bodies also perturb the orbits of LISA spacecraft and affect the time delay interferometry (TDI), we simulate the time delay numerically in this paper for all solutions with the generation number n ⩽ 3. We have worked out a set of 3-year optimized mission orbits of LISA spacecraft starting at January 1, 2021 using the CGC2.7 ephemeris framework. We then use this numerical solution to calculate the residual optical path differences in the second-generation solutions of our previous paper, and compare with the semi-analytic error estimate. The accuracy of this calculation is better than 1 cm (or 30 ps). The maximum path length difference, for all configuration calculated, is below 1 m (3 ns). This is well below the limit under which the laser frequency noise is required to be suppressed. The numerical simulation in this paper can be applied to other space-borne interferometers for gravitational wave detection with the simplification of having only one interferometer.

Intercomparison of 3D pore-scale flow and solute transport simulation methods

DOE PAGES

Mehmani, Yashar; Schoenherr, Martin; Pasquali, Andrea; ...

2015-09-28

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based onmore » the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This paper provides support for confidence in a variety of pore-scale modeling methods and motivates further development and application of pore-scale simulation methods.« less

Intercomparison of 3D pore-scale flow and solute transport simulation methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaofan; Mehmani, Yashar; Perkins, William A.

2016-09-01

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based onmore » the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This study provides support for confidence in a variety of pore-scale modeling methods and motivates further development and application of pore-scale simulation methods.« less

Study of Magnetic Damping Effect on Convection and Solidification Under G-Jitter Conditions

NASA Technical Reports Server (NTRS)

Li, Ben Q.; deGroh, H. C., III

1999-01-01

As shown by NASA resources dedicated to measuring residual gravity (SAMS and OARE systems), g-jitter is a critical issue affecting space experiments on solidification processing of materials. This study aims to provide, through extensive numerical simulations and ground based experiments, an assessment of the use of magnetic fields in combination with microgravity to reduce the g-jitter induced convective flows in space processing systems. We have so far completed asymptotic analyses based on the analytical solutions for g-jitter driven flow and magnetic field damping effects for a simple one-dimensional parallel plate configuration, and developed both 2-D and 3-D numerical models for g-jitter driven flows in simple solidification systems with and without presence of an applied magnetic field. Numerical models have been checked with the analytical solutions and have been applied to simulate the convective flows and mass transfer using both synthetic g-jitter functions and the g-jitter data taken from space flight. Some useful findings have been obtained from the analyses and the modeling results. Some key points may be summarized as follows: (1) the amplitude of the oscillating velocity decreases at a rate inversely proportional to the g-jitter frequency and with an increase in the applied magnetic field; (2) the induced flow approximately oscillates at the same frequency as the affecting g-jitter, but out of a phase angle; (3) the phase angle is a complicated function of geometry, applied magnetic field, temperature gradient and frequency; (4) g-jitter driven flows exhibit a complex fluid flow pattern evolving in time; (5) the damping effect is more effective for low frequency flows; and (6) the applied magnetic field helps to reduce the variation of solutal distribution along the solid-liquid interface. Work in progress includes numerical simulations and ground-based measurements. Both 2-D and 3-D numerical simulations are being continued to obtain further information on g-jitter driven flows and magnetic field effects. A physical model for ground-based measurements is completed and some measurements of the oscillating convection are being taken on the physical model. The comparison of the measurements with numerical simulations is in progress. Additional work planned in the project will also involve extending the 2-D numerical model to include the solidification phenomena with the presence of both g-jitter and magnetic fields.

Applications of Analytical Self-Similar Solutions of Reynolds-Averaged Models for Instability-Induced Turbulent Mixing

NASA Astrophysics Data System (ADS)

Hartland, Tucker; Schilling, Oleg

2017-11-01

Analytical self-similar solutions to several families of single- and two-scale, eddy viscosity and Reynolds stress turbulence models are presented for Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instability-induced turbulent mixing. The use of algebraic relationships between model coefficients and physical observables (e.g., experimental growth rates) following from the self-similar solutions to calibrate a member of a given family of turbulence models is shown. It is demonstrated numerically that the algebraic relations accurately predict the value and variation of physical outputs of a Reynolds-averaged simulation in flow regimes that are consistent with the simplifying assumptions used to derive the solutions. The use of experimental and numerical simulation data on Reynolds stress anisotropy ratios to calibrate a Reynolds stress model is briefly illustrated. The implications of the analytical solutions for future Reynolds-averaged modeling of hydrodynamic instability-induced mixing are briefly discussed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Numerical Simulation of Interaction of Human Vocal Folds and Fluid Flow

NASA Astrophysics Data System (ADS)

Kosík, A.; Feistauer, M.; Horáček, J.; Sváček, P.

Our goal is to simulate airflow in human vocal folds and their flow-induced vibrations. We consider two-dimensional viscous incompressible flow in a time-dependent domain. The fluid flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation. The flow problem is coupled with the elastic behaviour of the solid bodies. The developed solution of the coupled problem based on the finite element method is demonstrated by numerical experiments.

Stochastic analysis of multiphase flow in porous media: II. Numerical simulations

NASA Astrophysics Data System (ADS)

Abin, A.; Kalurachchi, J. J.; Kemblowski, M. W.; Chang, C.-M.

1996-08-01

The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, α. These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter α. The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.

On the Minimal Accuracy Required for Simulating Self-gravitating Systems by Means of Direct N-body Methods

NASA Astrophysics Data System (ADS)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-01

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-body interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.

Numerical simulation of flow through the Langley parametric scramjet engine

NASA Technical Reports Server (NTRS)

Srinivasan, Shivakumar; Kamath, Pradeep S.; Mcclinton, Charles R.

1989-01-01

The numerical simulation of a three-dimensional turbulent, reacting flow through the entire Langley parametric scramjet engine has been obtained using a piecewise elliptic approach. The last section in the combustor has been analyzed using a parabolized Navier-Stokes code. The facility nozzle flow was analyzed as a first step. The outflow conditions from the nozzle were chosen as the inflow conditions of the scramjet inlet. The nozzle and the inlet simulation were accomplished by solving the three-dimensional Navier-Stokes equations with a perfect gas assumption. The inlet solution downstream of the scramjet throat was used to provide inflow conditions for the combustor region. The first two regions of the combustor were analyzed using the MacCormack's explicit scheme. However, the source terms in the species equations were solved implicitly. The finite rate chemistry was modeled using the two-step reaction model of Rogers and Chinitz. A complete reaction model was used in the PNS code to solve the last combustor region. The numerical solutions provide an insight of the flow details in a complete hydrogen-fueled scramjet engine module.

Towards wall functions for the prediction of solute segregation in plane front directional solidification

NASA Astrophysics Data System (ADS)

Chatelain, M.; Rhouzlane, S.; Botton, V.; Albaric, M.; Henry, D.; Millet, S.; Pelletier, D.; Garandet, J. P.

2017-10-01

The present paper focuses on solute segregation occurring in directional solidification processes with sharp solid/liquid interface, like silicon crystal growth. A major difficulty for the simulation of such processes is their inherently multi-scale nature: the impurity segregation problem is controlled at the solute boundary layer scale (micrometers) while the thermal problem is ruled at the crucible scale (meters). The thickness of the solute boundary layer is controlled by the convection regime and requires a specific refinement of the mesh of numerical models. In order to improve numerical simulations, wall functions describing solute boundary layers for convecto-diffusive regimes are derived from a scaling analysis. The aim of these wall functions is to obtain segregation profiles from purely thermo-hydrodynamic simulations, which do not require solute boundary layer refinement at the solid/liquid interface. Regarding industrial applications, various stirring techniques can be used to enhance segregation, leading to fully turbulent flows in the melt. In this context, the scaling analysis is further improved by taking into account the turbulent solute transport. The solute boundary layers predicted by the analytical model are compared to those obtained by transient segregation simulations in a canonical 2D lid driven cavity configuration for validation purposes. Convective regimes ranging from laminar to fully turbulent are considered. Growth rate and molecular diffusivity influences are also investigated. Then, a procedure to predict concentration fields in the solid phase from a hydrodynamic simulation of the solidification process is proposed. This procedure is based on the analytical wall functions and on solute mass conservation. It only uses wall shear-stress profiles at the solidification front as input data. The 2D analytical concentration fields are directly compared to the results of the complete simulation of segregation in the lid driven cavity configuration. Finally, an additional output from the analytical model is also presented. We put in light the correlation between different species convecto-diffusive behaviour; we use it to propose an estimation method for the segregation parameters of various chemical species knowing segregation parameters of one specific species.

Cosmic strings - A problem or a solution?

NASA Technical Reports Server (NTRS)

Bennett, David P.; Bouchet, Francois R.

1988-01-01

The most fundamental issue in the theory of cosmic strings is addressed by means of Numerical Simulations: the existence of a scaling solution. The resolution of this question will determine whether cosmic strings can form the basis of an attractive theory of galaxy formation or prove to be a cosmological disaster like magnetic monopoles or domain walls. After a brief discussion of our numerical technique, results are presented which, though still preliminary, offer the best support to date of this scaling hypothesis.

Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

USGS Publications Warehouse

Weatherill, D.; Simmons, C.T.; Voss, C.I.; Robinson, N.I.

2004-01-01

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA-A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4??2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. ?? 2004 Elsevier Ltd. All rights reserved.

A coupled ALE-AMR method for shock hydrodynamics

DOE PAGES

Waltz, J.; Bakosi, J.

2018-03-05

We present a numerical method combining adaptive mesh refinement (AMR) with arbitrary Lagrangian-Eulerian (ALE) mesh motion for the simulation of shock hydrodynamics on unstructured grids. The primary goal of the coupled method is to use AMR to reduce numerical error in ALE simulations at reduced computational expense relative to uniform fine mesh calculations, in the same manner that AMR has been used in Eulerian simulations. We also identify deficiencies with ALE methods that AMR is able to mitigate, and discuss the unique coupling challenges. The coupled method is demonstrated using three-dimensional unstructured meshes of up to O(10 7) tetrahedral cells.more » Convergence of ALE-AMR solutions towards both uniform fine mesh ALE results and analytic solutions is demonstrated. Speed-ups of 5-10× for a given level of error are observed relative to uniform fine mesh calculations.« less

A coupled ALE-AMR method for shock hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Waltz, J.; Bakosi, J.

We present a numerical method combining adaptive mesh refinement (AMR) with arbitrary Lagrangian-Eulerian (ALE) mesh motion for the simulation of shock hydrodynamics on unstructured grids. The primary goal of the coupled method is to use AMR to reduce numerical error in ALE simulations at reduced computational expense relative to uniform fine mesh calculations, in the same manner that AMR has been used in Eulerian simulations. We also identify deficiencies with ALE methods that AMR is able to mitigate, and discuss the unique coupling challenges. The coupled method is demonstrated using three-dimensional unstructured meshes of up to O(10 7) tetrahedral cells.more » Convergence of ALE-AMR solutions towards both uniform fine mesh ALE results and analytic solutions is demonstrated. Speed-ups of 5-10× for a given level of error are observed relative to uniform fine mesh calculations.« less

Spinning solutions in general relativity with infinite central density

NASA Astrophysics Data System (ADS)

Flammer, P. D.

2018-05-01

This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical differential equations. Due to the logarithmic scale, we can resolve solutions with near-singular mass distributions near their center, while the solution domain extends many orders of magnitude larger than the radius of the distribution (to connect with flat space-time). Rotating solutions are found with very high central energy densities for a range of adiabatic exponents. Analytically, assuming the pressure is proportional to the energy density (which is true for polytropes in the limit of large energy density), we determine the small radius behavior of the metric potentials and energy density. This small radius behavior agrees well with the small radius behavior of large central density numerical results, lending confidence to our numerical approach. We compare results with rotating solutions available in the literature, which show good agreement. We study the stability of spherical solutions: instability sets in at the first maximum in mass versus central energy density; this is also consistent with results in the literature, and further lends confidence to the numerical approach.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

Existence of periodic solutions in a model of respiratory syncytial virus RSV

NASA Astrophysics Data System (ADS)

Arenas, Abraham J.; González, Gilberto; Jódar, Lucas

2008-08-01

In this paper we study the existence of a positive periodic solutions for nested models of respiratory syncytial virus RSV, by using a continuation theorem based on coincidence degree theory. Conditions for the existence of periodic solutions in the model are given. Numerical simulations related to the transmission of respiratory syncytial virus in Madrid and Rio Janeiro are included.

On the Possibilities of Predicting Geomagnetic Secular Variation with Geodynamo Modeling

NASA Technical Reports Server (NTRS)

Kuang, Wei-Jia; Tangborn, Andrew; Sabaka, Terrance

2004-01-01

We use our MoSST core dynamics model and geomagnetic field at the core-mantle boundary (CMB) continued downward from surface observations to investigate possibilities of geomagnetic data assimilation, so that model results and current geomagnetic observations can be used to predict geomagnetic secular variation in future. As the first attempt, we apply data insertion technique to examine evolution of the model solution that is modified by geomagnetic input. Our study demonstrate that, with a single data insertion, large-scale poloidal magnetic field obtained from subsequent numerical simulation evolves similarly to the observed geomagnetic variation, regardless of the initial choice of the model solution (so long it is a well developed numerical solution). The model solution diverges on the time scales on the order of 60 years, similar to the time scales of the torsional oscillations in the Earth's core. Our numerical test shows that geomagnetic data assimilation is promising with our MoSST model.

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Numerical solution of the full potential equation using a chimera grid approach

NASA Technical Reports Server (NTRS)

Holst, Terry L.

1995-01-01

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation.

PubMed

Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

2014-11-25

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

Comparative analysis of numerical simulation techniques for incoherent imaging of extended objects through atmospheric turbulence

NASA Astrophysics Data System (ADS)

Lachinova, Svetlana L.; Vorontsov, Mikhail A.; Filimonov, Grigory A.; LeMaster, Daniel A.; Trippel, Matthew E.

2017-07-01

Computational efficiency and accuracy of wave-optics-based Monte-Carlo and brightness function numerical simulation techniques for incoherent imaging of extended objects through atmospheric turbulence are evaluated. Simulation results are compared with theoretical estimates based on known analytical solutions for the modulation transfer function of an imaging system and the long-exposure image of a Gaussian-shaped incoherent light source. It is shown that the accuracy of both techniques is comparable over the wide range of path lengths and atmospheric turbulence conditions, whereas the brightness function technique is advantageous in terms of the computational speed.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

Contact Line Dynamics

NASA Astrophysics Data System (ADS)

Kreiss, Gunilla; Holmgren, Hanna; Kronbichler, Martin; Ge, Anthony; Brant, Luca

2017-11-01

The conventional no-slip boundary condition leads to a non-integrable stress singularity at a moving contact line. This makes numerical simulations of two-phase flow challenging, especially when capillarity of the contact point is essential for the dynamics of the flow. We will describe a modeling methodology, which is suitable for numerical simulations, and present results from numerical computations. The methodology is based on combining a relation between the apparent contact angle and the contact line velocity, with the similarity solution for Stokes flow at a planar interface. The relation between angle and velocity can be determined by theoretical arguments, or from simulations using a more detailed model. In our approach we have used results from phase field simulations in a small domain, but using a molecular dynamics model should also be possible. In both cases more physics is included and the stress singularity is removed.

Efficient and Robust Optimization for Building Energy Simulation

PubMed Central

Pourarian, Shokouh; Kearsley, Anthony; Wen, Jin; Pertzborn, Amanda

2016-01-01

Efficiently, robustly and accurately solving large sets of structured, non-linear algebraic and differential equations is one of the most computationally expensive steps in the dynamic simulation of building energy systems. Here, the efficiency, robustness and accuracy of two commonly employed solution methods are compared. The comparison is conducted using the HVACSIM+ software package, a component based building system simulation tool. The HVACSIM+ software presently employs Powell’s Hybrid method to solve systems of nonlinear algebraic equations that model the dynamics of energy states and interactions within buildings. It is shown here that the Powell’s method does not always converge to a solution. Since a myriad of other numerical methods are available, the question arises as to which method is most appropriate for building energy simulation. This paper finds considerable computational benefits result from replacing the Powell’s Hybrid method solver in HVACSIM+ with a solver more appropriate for the challenges particular to numerical simulations of buildings. Evidence is provided that a variant of the Levenberg-Marquardt solver has superior accuracy and robustness compared to the Powell’s Hybrid method presently used in HVACSIM+. PMID:27325907

Efficient and Robust Optimization for Building Energy Simulation.

PubMed

Pourarian, Shokouh; Kearsley, Anthony; Wen, Jin; Pertzborn, Amanda

2016-06-15

Efficiently, robustly and accurately solving large sets of structured, non-linear algebraic and differential equations is one of the most computationally expensive steps in the dynamic simulation of building energy systems. Here, the efficiency, robustness and accuracy of two commonly employed solution methods are compared. The comparison is conducted using the HVACSIM+ software package, a component based building system simulation tool. The HVACSIM+ software presently employs Powell's Hybrid method to solve systems of nonlinear algebraic equations that model the dynamics of energy states and interactions within buildings. It is shown here that the Powell's method does not always converge to a solution. Since a myriad of other numerical methods are available, the question arises as to which method is most appropriate for building energy simulation. This paper finds considerable computational benefits result from replacing the Powell's Hybrid method solver in HVACSIM+ with a solver more appropriate for the challenges particular to numerical simulations of buildings. Evidence is provided that a variant of the Levenberg-Marquardt solver has superior accuracy and robustness compared to the Powell's Hybrid method presently used in HVACSIM+.

Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

NASA Astrophysics Data System (ADS)

Lucas-Serrano, A.; Font, J. A.; Ibáñez, J. M.; Martí, J. M.

2004-12-01

We assess the suitability of a recent high-resolution central scheme developed by \\cite{kurganov} for the solution of the relativistic hydrodynamic equations. The novelty of this approach relies on the absence of Riemann solvers in the solution procedure. The computations we present are performed in one and two spatial dimensions in Minkowski spacetime. Standard numerical experiments such as shock tubes and the relativistic flat-faced step test are performed. As an astrophysical application the article includes two-dimensional simulations of the propagation of relativistic jets using both Cartesian and cylindrical coordinates. The simulations reported clearly show the capabilities of the numerical scheme of yielding satisfactory results, with an accuracy comparable to that obtained by the so-called high-resolution shock-capturing schemes based upon Riemann solvers (Godunov-type schemes), even well inside the ultrarelativistic regime. Such a central scheme can be straightforwardly applied to hyperbolic systems of conservation laws for which the characteristic structure is not explicitly known, or in cases where a numerical computation of the exact solution of the Riemann problem is prohibitively expensive. Finally, we present comparisons with results obtained using various Godunov-type schemes as well as with those obtained using other high-resolution central schemes which have recently been reported in the literature.

Metrics for comparing dynamic earthquake rupture simulations

USGS Publications Warehouse

Barall, Michael; Harris, Ruth A.

2014-01-01

Earthquakes are complex events that involve a myriad of interactions among multiple geologic features and processes. One of the tools that is available to assist with their study is computer simulation, particularly dynamic rupture simulation. A dynamic rupture simulation is a numerical model of the physical processes that occur during an earthquake. Starting with the fault geometry, friction constitutive law, initial stress conditions, and assumptions about the condition and response of the near‐fault rocks, a dynamic earthquake rupture simulation calculates the evolution of fault slip and stress over time as part of the elastodynamic numerical solution (Ⓔ see the simulation description in the electronic supplement to this article). The complexity of the computations in a dynamic rupture simulation make it challenging to verify that the computer code is operating as intended, because there are no exact analytic solutions against which these codes’ results can be directly compared. One approach for checking if dynamic rupture computer codes are working satisfactorily is to compare each code’s results with the results of other dynamic rupture codes running the same earthquake simulation benchmark. To perform such a comparison consistently, it is necessary to have quantitative metrics. In this paper, we present a new method for quantitatively comparing the results of dynamic earthquake rupture computer simulation codes.

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Touma, Rony; Zeidan, Dia

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potentialmore » of the proposed scheme.« less

Validation of the enthalpy method by means of analytical solution

NASA Astrophysics Data System (ADS)

Kleiner, Thomas; Rückamp, Martin; Bondzio, Johannes; Humbert, Angelika

2014-05-01

Numerical simulations moved in the recent year(s) from describing the cold-temperate transition surface (CTS) towards an enthalpy description, which allows avoiding incorporating a singular surface inside the model (Aschwanden et al., 2012). In Enthalpy methods the CTS is represented as a level set of the enthalpy state variable. This method has several numerical and practical advantages (e.g. representation of the full energy by one scalar field, no restriction to topology and shape of the CTS). The proposed method is rather new in glaciology and to our knowledge not verified and validated against analytical solutions. Unfortunately we are still lacking analytical solutions for sufficiently complex thermo-mechanically coupled polythermal ice flow. However, we present two experiments to test the implementation of the enthalpy equation and corresponding boundary conditions. The first experiment tests particularly the functionality of the boundary condition scheme and the corresponding basal melt rate calculation. Dependent on the different thermal situations that occur at the base, the numerical code may have to switch to another boundary type (from Neuman to Dirichlet or vice versa). The main idea of this set-up is to test the reversibility during transients. A former cold ice body that run through a warmer period with an associated built up of a liquid water layer at the base must be able to return to its initial steady state. Since we impose several assumptions on the experiment design analytical solutions can be formulated for different quantities during distinct stages of the simulation. The second experiment tests the positioning of the internal CTS in a parallel-sided polythermal slab. We compare our simulation results to the analytical solution proposed by Greve and Blatter (2009). Results from three different ice flow-models (COMIce, ISSM, TIMFD3) are presented.

LES-ODT Simulations of Turbulent Reacting Shear Layers

NASA Astrophysics Data System (ADS)

Hoffie, Andreas; Echekki, Tarek

2012-11-01

Large-eddy simulations (LES) combined with the one-dimensional turbulence (ODT) simulations of a spatially developing turbulent reacting shear layer with heat release and high Reynolds numbers were conducted and compared to results from direct numerical simulations (DNS) of the same configuration. The LES-ODT approach is based on LES solutions for momentum on a coarse grid and solutions for momentum and reactive scalars on a fine ODT grid, which is embedded in the LES computational domain. The shear layer is simulated with a single-step, second-order reaction with an Arrhenius reaction rate. The transport equations are solved using a low Mach number approximation. The LES-ODT simulations yield reasonably accurate predictions of turbulence and passive/reactive scalars' statistics compared to DNS results.

Dynamics of Numerics & Spurious Behaviors in CFD Computations. Revised

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Sweby, Peter K.

1997-01-01

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

A new numerical benchmark for variably saturated variable-density flow and transport in porous media

NASA Astrophysics Data System (ADS)

Guevara, Carlos; Graf, Thomas

2016-04-01

In subsurface hydrological systems, spatial and temporal variations in solute concentration and/or temperature may affect fluid density and viscosity. These variations could lead to potentially unstable situations, in which a dense fluid overlies a less dense fluid. These situations could produce instabilities that appear as dense plume fingers migrating downwards counteracted by vertical upwards flow of freshwater (Simmons et al., Transp. Porous Medium, 2002). As a result of unstable variable-density flow, solute transport rates are increased over large distances and times as compared to constant-density flow. The numerical simulation of variable-density flow in saturated and unsaturated media requires corresponding benchmark problems against which a computer model is validated (Diersch and Kolditz, Adv. Water Resour, 2002). Recorded data from a laboratory-scale experiment of variable-density flow and solute transport in saturated and unsaturated porous media (Simmons et al., Transp. Porous Medium, 2002) is used to define a new numerical benchmark. The HydroGeoSphere code (Therrien et al., 2004) coupled with PEST (www.pesthomepage.org) are used to obtain an optimized parameter set capable of adequately representing the data set by Simmons et al., (2002). Fingering in the numerical model is triggered using random hydraulic conductivity fields. Due to the inherent randomness, a large number of simulations were conducted in this study. The optimized benchmark model adequately predicts the plume behavior and the fate of solutes. This benchmark is useful for model verification of variable-density flow problems in saturated and/or unsaturated media.

Terahertz response of dipolar impurities in polar liquids: On anomalous dielectric absorption of protein solutions

NASA Astrophysics Data System (ADS)

Matyushov, Dmitry V.

2010-02-01

A theory of radiation absorption by dielectric mixtures is presented. The coarse-grained formulation is based on the wave-vector-dependent correlation functions of molecular dipoles of the host polar liquid and a density structure factor of the solutes. A nonlinear dependence of the dielectric absorption coefficient on the solute concentration is predicted and originates from the mutual polarization of the liquid surrounding the solutes by the collective field of the solute dipoles aligned along the radiation field. The theory is applied to terahertz absorption of hydrated saccharides and proteins. While the theory gives an excellent account of the observations for saccharides, without additional assumptions and fitting parameters, experimental absorption coefficient of protein solutions significantly exceeds theoretical calculations with dipole moment of the bare protein assigned to the solute and shows a peak against the protein concentration. A substantial polarization of protein’s hydration shell, resulting in a net dipole moment, is required to explain the disagreement between theory and experiment. When the correlation function of the total dipole moment of the protein with its hydration shell from numerical simulations is used in the analytical model, an absorption peak, qualitatively similar to that seen in experiment, is obtained. The existence and position of the peak are sensitive to the specifics of the protein-protein interactions. Numerical testing of the theory requires the combination of dielectric and small-angle scattering measurements. The calculations confirm that “elastic ferroelectric bag” of water shells observed in previous numerical simulations is required to explain terahertz dielectric measurements.

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

NASA Technical Reports Server (NTRS)

Bui, Trong T.

1999-01-01

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

Forebody and base region real gas flow in severe planetary entry by a factored implicit numerical method. II - Equilibrium reactive gas

NASA Technical Reports Server (NTRS)

Davy, W. C.; Green, M. J.; Lombard, C. K.

1981-01-01

The factored-implicit, gas-dynamic algorithm has been adapted to the numerical simulation of equilibrium reactive flows. Changes required in the perfect gas version of the algorithm are developed, and the method of coupling gas-dynamic and chemistry variables is discussed. A flow-field solution that approximates a Jovian entry case was obtained by this method and compared with the same solution obtained by HYVIS, a computer program much used for the study of planetary entry. Comparison of surface pressure distribution and stagnation line shock-layer profiles indicates that the two solutions agree well.

A study on the behaviour of high-order flux reconstruction method with different low-dissipation numerical fluxes for large eddy simulation

NASA Astrophysics Data System (ADS)

Boxi, Lin; Chao, Yan; Shusheng, Chen

2017-10-01

This work focuses on the numerical dissipation features of high-order flux reconstruction (FR) method combined with different numerical fluxes in turbulence flows. The famous Roe and AUSM+ numerical fluxes together with their corresponding low-dissipation enhanced versions (LMRoe, SLAU2) and higher resolution variants (HR-LMRoe, HR-SLAU2) are incorporated into FR framework, and the dissipation interplay of these combinations is investigated in implicit large eddy simulation. The numerical dissipation stemming from these convective numerical fluxes is quantified by simulating the inviscid Gresho vortex, the transitional Taylor-Green vortex and the homogenous decaying isotropic turbulence. The results suggest that low-dissipation enhanced versions are preferential both in high-order and low-order cases to their original forms, while the use of HR-SLAU2 has marginal improvements and the HR-LMRoe leads to degenerated solution with high-order. In high-order the effects of numerical fluxes are reduced, and their viscosity may not be dissipative enough to provide physically consistent turbulence when under-resolved.

High Order Finite Difference Methods with Subcell Resolution for 2D Detonation Waves

NASA Technical Reports Server (NTRS)

Wang, W.; Shu, C. W.; Yee, H. C.; Sjogreen, B.

2012-01-01

In simulating hyperbolic conservation laws in conjunction with an inhomogeneous stiff source term, if the solution is discontinuous, spurious numerical results may be produced due to different time scales of the transport part and the source term. This numerical issue often arises in combustion and high speed chemical reacting flows.

Simulation of ground-water flow and solute transport in the Glen Canyon aquifer, East-Central Utah

USGS Publications Warehouse

Freethey, Geoffrey W.; Stolp, Bernard J.

2010-01-01

The extraction of methane from coal beds in the Ferron coal trend in central Utah started in the mid-1980s. Beginning in 1994, water from the extraction process was pressure injected into the Glen Canyon aquifer. The lateral extent of the aquifer that could be affected by injection is about 7,600 square miles. To address regional-scale effects of injection over a decadal time frame, a conceptual model of ground-water movement and transport of dissolved solids was formulated. A numerical model that incorporates aquifer concepts was then constructed and used to simulate injection.The Glen Canyon aquifer within the study area is conceptualized in two parts—an active area of ground-water flow and solute transport that exists between recharge areas in the San Rafael Swell and Desert, Waterpocket Fold, and Henry Mountains and discharge locations along the Muddy, Dirty Devil, San Rafael, and Green Rivers. An area of little or negligible ground-water flow exists north of Price, Utah, and beneath the Wasatch Plateau. Pressurized injection of coal-bed methane production water occurs in this area where dissolved-solids concentrations can be more than 100,000 milligrams per liter. Injection has the potential to increase hydrologic interaction with the active flow area, where dissolved-solids concentrations are generally less than 3,000 milligrams per liter.Pressurized injection of coal-bed methane production water in 1994 initiated a net addition of flow and mass of solutes into the Glen Canyon aquifer. To better understand the regional scale hydrologic interaction between the two areas of the Glen Canyon aquifer, pressurized injection was numerically simulated. Data constraints precluded development of a fully calibrated simulation; instead, an uncalibrated model was constructed that is a plausible representation of the conceptual flow and solute-transport processes. The amount of injected water over the 36-year simulation period is about 25,000 acre-feet. As a result, simulated water levels in the injection areas increased by 50 feet and dissolved-solids concentrations increased by 100 milligrams per liter or more. These increases are accrued into aquifer storage and do not extend to the rivers during the 36-year simulation period. The amount of change in simulated discharge and solute load to the rivers is less than the resolution accuracy of the numerical simulation and is interpreted as no significant change over the considered time period.

Stabilized finite element methods to simulate the conductances of ion channels

NASA Astrophysics Data System (ADS)

Tu, Bin; Xie, Yan; Zhang, Linbo; Lu, Benzhuo

2015-03-01

We have previously developed a finite element simulator, ichannel, to simulate ion transport through three-dimensional ion channel systems via solving the Poisson-Nernst-Planck equations (PNP) and Size-modified Poisson-Nernst-Planck equations (SMPNP), and succeeded in simulating some ion channel systems. However, the iterative solution between the coupled Poisson equation and the Nernst-Planck equations has difficulty converging for some large systems. One reason we found is that the NP equations are advection-dominated diffusion equations, which causes troubles in the usual FE solution. The stabilized schemes have been applied to compute fluids flow in various research fields. However, they have not been studied in the simulation of ion transport through three-dimensional models based on experimentally determined ion channel structures. In this paper, two stabilized techniques, the SUPG and the Pseudo Residual-Free Bubble function (PRFB) are introduced to enhance the numerical robustness and convergence performance of the finite element algorithm in ichannel. The conductances of the voltage dependent anion channel (VDAC) and the anthrax toxin protective antigen pore (PA) are simulated to validate the stabilization techniques. Those two stabilized schemes give reasonable results for the two proteins, with decent agreement with both experimental data and Brownian dynamics (BD) simulations. For a variety of numerical tests, it is found that the simulator effectively avoids previous numerical instability after introducing the stabilization methods. Comparison based on our test data set between the two stabilized schemes indicates both SUPG and PRFB have similar performance (the latter is slightly more accurate and stable), while SUPG is relatively more convenient to implement.

Panel summary report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gutjahr, A.L.; Kincaid, C.T.; Mercer, J.W.

1987-04-01

The objective of this report is to summarize the various modeling approaches that were used to simulate solute transport in a variably saturated emission. In particular, the technical strengths and weaknesses of each approach are discussed, and conclusions and recommendations for future studies are made. Five models are considered: (1) one-dimensional analytical and semianalytical solutions of the classical deterministic convection-dispersion equation (van Genuchten, Parker, and Kool, this report ); (2) one-dimensional simulation using a continuous-time Markov process (Knighton and Wagenet, this report); (3) one-dimensional simulation using the time domain method and the frequency domain method (Duffy and Al-Hassan, this report);more » (4) one-dimensional numerical approach that combines a solution of the classical deterministic convection-dispersion equation with a chemical equilibrium speciation model (Cederberg, this report); and (5) three-dimensional numerical solution of the classical deterministic convection-dispersion equation (Huyakorn, Jones, Parker, Wadsworth, and White, this report). As part of the discussion, the input data and modeling results are summarized. The models were used in a data analysis mode, as opposed to a predictive mode. Thus, the following discussion will concentrate on the data analysis aspects of model use. Also, all the approaches were similar in that they were based on a convection-dispersion model of solute transport. Each discussion addresses the modeling approaches in the order listed above.« less

Computational issues in the simulation of two-dimensional discrete dislocation mechanics

NASA Astrophysics Data System (ADS)

Segurado, J.; LLorca, J.; Romero, I.

2007-06-01

The effect of the integration time step and the introduction of a cut-off velocity for the dislocation motion was analysed in discrete dislocation dynamics (DD) simulations of a single crystal microbeam. Two loading modes, bending and uniaxial tension, were examined. It was found that a longer integration time step led to a progressive increment of the oscillations in the numerical solution, which would eventually diverge. This problem could be corrected in the simulations carried out in bending by introducing a cut-off velocity for the dislocation motion. This strategy (long integration times and a cut-off velocity for the dislocation motion) did not recover, however, the solution computed with very short time steps in uniaxial tension: the dislocation density was overestimated and the dislocation patterns modified. The different response to the same numerical algorithm was explained in terms of the nature of the dislocations generated in each case: geometrically necessary in bending and statistically stored in tension. The evolution of the dislocation density in the former was controlled by the plastic curvature of the beam and was independent of the details of the simulations. On the contrary, the steady-state dislocation density in tension was determined by the balance between nucleation of dislocations and those which are annihilated or which exit the beam. Changes in the DD imposed by the cut-off velocity altered this equilibrium and the solution. These results point to the need for detailed analyses of the accuracy and stability of the dislocation dynamic simulations to ensure that the results obtained are not fundamentally affected by the numerical strategies used to solve this complex problem.

Comment on high resolution simulations of cosmic strings. 1: Network evoloution

NASA Technical Reports Server (NTRS)

Turok, Neil; Albrecht, Andreas

1990-01-01

Comments are made on recent claims (Albrecht and Turok, 1989) regarding simulations of cosmic string evolution. Specially, it was claimed that results were dominated by a numerical artifact which rounds out kinks on a scale of the order of the correlation length on the network. This claim was based on an approximate analysis of an interpolation equation which is solved herein. The typical rounding scale is actually less than one fifth of the correlation length, and comparable with other numerical cutoffs. Results confirm previous estimates of numerical uncertainties, and show that the approximations poorly represent the real solutions to the interpolation equation.

Numerical Simulation for the Unsteady MHD Flow and Heat Transfer of Couple Stress Fluid over a Rotating Disk

PubMed Central

2014-01-01

The present work is devoted to study the numerical simulation for unsteady MHD flow and heat transfer of a couple stress fluid over a rotating disk. A similarity transformation is employed to reduce the time dependent system of nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). The Runge-Kutta method and shooting technique are employed for finding the numerical solution of the governing system. The influences of governing parameters viz. unsteadiness parameter, couple stress and various physical parameters on velocity, temperature and pressure profiles are analyzed graphically and discussed in detail. PMID:24835274

Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg Landau equation with variable coefficients

NASA Astrophysics Data System (ADS)

Fang, Fang; Xiao, Yan

2006-12-01

We consider an inhomogeneous optical fiber system described by the generalized cubic complex Ginzburg-Landau (CGL) equation with varying dispersion, nonlinearity, gain (loss), nonlinear gain (absorption) and the effect of spectral limitation. Exact chirped bright and dark soliton-like solutions of the CGL equation were found by using a suitable ansatz. Furthermore, we analyze the features of the solitons and consider the problem of stability of these soliton-like solutions under finite initial perturbations. It is shown by extensive numerical simulations that both bright and dark soliton-like solutions are stable in an inhomogeneous fiber system. Finally, the interaction between two chirped bright and dark soliton-like pulses is investigated numerically.

A new approach to exact optical soliton solutions for the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Baleanu, Dumitru

2018-05-01

By using the modified homotopy analysis transform method, we construct the analytical solutions of the space-time generalized nonlinear Schrödinger equation involving a new fractional conformable derivative in the Liouville-Caputo sense and the fractional-order derivative with the Mittag-Leffler law. Employing theoretical parameters, we present some numerical simulations and compare the solutions obtained.

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Numerical simulation of double‐diffusive finger convection

USGS Publications Warehouse

Hughes, Joseph D.; Sanford, Ward E.; Vacher, H. Leonard

2005-01-01

A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double‐diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density‐dependent, saturated‐unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute‐transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute‐transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High‐resolution data from a double‐diffusive Hele‐Shaw experiment, initially in a density‐stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double‐diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer.

Numerical Experiments in Error Control for Sound Propagation Using a Damping Layer Boundary Treatment

NASA Technical Reports Server (NTRS)

Goodrich, John W.

2017-01-01

This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].

Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping

2016-10-01

Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.

Mass transfer in thin films under counter-current gas: experiments and numerical study

NASA Astrophysics Data System (ADS)

Lucquiaud, Mathieu; Lavalle, Gianluca; Schmidt, Patrick; Ausner, Ilja; Wehrli, Marc; O Naraigh, Lennon; Valluri, Prashant

2016-11-01

Mass transfer in liquid-gas stratified flows is strongly affected by the waviness of the interface. For reactive flows, the chemical reactions occurring at the liquid-gas interface also influence the mass transfer rate. This is encountered in several technological applications, such as absorption units for carbon capture. We investigate the absorption rate of carbon dioxide in a liquid solution. The experimental set-up consists of a vertical channel where a falling film is sheared by a counter-current gas flow. We measure the absorption occurring at different flow conditions, by changing the liquid solution, the liquid flow rate and the gas composition. With the aim to support the experimental results with numerical simulations, we implement in our level-set flow solver a novel module for mass transfer taking into account a variant of the ghost-fluid formalism. We firstly validate the pure mass transfer case with and without hydrodynamics by comparing the species concentration in the bulk flow to the analytical solution. In a final stage, we analyse the absorption rate in reactive flows, and try to reproduce the experimental results by means of numerical simulations to explore the active role of the waves at the interface.

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

NASA Technical Reports Server (NTRS)

Bui, Trong T.; Mankbadi, Reda R.

1995-01-01

Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

Analytical approximation and numerical simulations for periodic travelling water waves

NASA Astrophysics Data System (ADS)

Kalimeris, Konstantinos

2017-12-01

We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity. This article is part of the theme issue 'Nonlinear water waves'.

Design of underwater robot lines based on a hybrid automatic optimization strategy

NASA Astrophysics Data System (ADS)

Lyu, Wenjing; Luo, Weilin

2014-09-01

In this paper, a hybrid automatic optimization strategy is proposed for the design of underwater robot lines. Isight is introduced as an integration platform. The construction of this platform is based on the user programming and several commercial software including UG6.0, GAMBIT2.4.6 and FLUENT12.0. An intelligent parameter optimization method, the particle swarm optimization, is incorporated into the platform. To verify the strategy proposed, a simulation is conducted on the underwater robot model 5470, which originates from the DTRC SUBOFF project. With the automatic optimization platform, the minimal resistance is taken as the optimization goal; the wet surface area as the constraint condition; the length of the fore-body, maximum body radius and after-body's minimum radius as the design variables. With the CFD calculation, the RANS equations and the standard turbulence model are used for direct numerical simulation. By analyses of the simulation results, it is concluded that the platform is of high efficiency and feasibility. Through the platform, a variety of schemes for the design of the lines are generated and the optimal solution is achieved. The combination of the intelligent optimization algorithm and the numerical simulation ensures a global optimal solution and improves the efficiency of the searching solutions.

Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry

USGS Publications Warehouse

Lewis, F.M.; Voss, C.I.; Rubin, Jacob

1986-01-01

A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)

Supercomputer modeling of flow past hypersonic flight vehicles

NASA Astrophysics Data System (ADS)

Ermakov, M. K.; Kryukov, I. A.

2017-02-01

A software platform for MPI-based parallel solution of the Navier-Stokes (Euler) equations for viscous heat-conductive compressible perfect gas on 3-D unstructured meshes is developed. The discretization and solution of the Navier-Stokes equations are constructed on generalized S.K. Godunov’s method and the second order approximation in space and time. Developed software platform allows to carry out effectively flow past hypersonic flight vehicles simulations for the Mach numbers 6 and higher, and numerical meshes with up to 1 billion numerical cells and with up to 128 processors.

A symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

NASA Astrophysics Data System (ADS)

Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.

2017-02-01

A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.

ON THE MINIMAL ACCURACY REQUIRED FOR SIMULATING SELF-GRAVITATING SYSTEMS BY MEANS OF DIRECT N-BODY METHODS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-10

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-bodymore » interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.« less

Numerical simulation of turbulent jet noise, part 2

NASA Technical Reports Server (NTRS)

Metcalfe, R. W.; Orszag, S. A.

1976-01-01

Results on the numerical simulation of jet flow fields were used to study the radiated sound field, and in addition, to extend and test the capabilities of the turbulent jet simulation codes. The principal result of the investigation was the computation of the radiated sound field from a turbulent jet. In addition, the computer codes were extended to account for the effects of compressibility and eddy viscosity, and the treatment of the nonlinear terms of the Navier-Stokes equations was modified so that they can be computed in a semi-implicit way. A summary of the flow model and a description of the numerical methods used for its solution are presented. Calculations of the radiated sound field are reported. In addition, the extensions that were made to the fundamental dynamical codes are described. Finally, the current state-of-the-art for computer simulation of turbulent jet noise is summarized.

Importance of inlet boundary conditions for numerical simulation of combustor flows

NASA Technical Reports Server (NTRS)

Sturgess, G. J.; Syed, S. A.; Mcmanus, K. R.

1983-01-01

Fluid dynamic computer codes for the mathematical simulation of problems in gas turbine engine combustion systems are required as design and diagnostic tools. To eventually achieve a performance standard with these codes of more than qualitative accuracy it is desirable to use benchmark experiments for validation studies. Typical of the fluid dynamic computer codes being developed for combustor simulations is the TEACH (Teaching Elliptic Axisymmetric Characteristics Heuristically) solution procedure. It is difficult to find suitable experiments which satisfy the present definition of benchmark quality. For the majority of the available experiments there is a lack of information concerning the boundary conditions. A standard TEACH-type numerical technique is applied to a number of test-case experiments. It is found that numerical simulations of gas turbine combustor-relevant flows can be sensitive to the plane at which the calculations start and the spatial distributions of inlet quantities for swirling flows.

A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry

NASA Astrophysics Data System (ADS)

Al-Marouf, M.; Samtaney, R.

2017-05-01

We present an embedded ghost fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

Direct numerical solution of the Ornstein-Zernike integral equation and spatial distribution of water around hydrophobic molecules

NASA Astrophysics Data System (ADS)

Ikeguchi, Mitsunori; Doi, Junta

1995-09-01

The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

Numerical Simulations of Particle Deposition in Metal Foam Heat Exchangers

NASA Astrophysics Data System (ADS)

Sauret, Emilie; Saha, Suvash C.; Gu, Yuantong

2013-01-01

Australia is a high-potential country for geothermal power with reserves currently estimated in the tens of millions of petajoules, enough to power the nation for at least 1000 years at current usage. However, these resources are mainly located in isolated arid regions where water is scarce. Therefore, wet cooling systems for geothermal plants in Australia are the least attractive solution and thus air-cooled heat exchangers are preferred. In order to increase the efficiency of such heat exchangers, metal foams have been used. One issue raised by this solution is the fouling caused by dust deposition. In this case, the heat transfer characteristics of the metal foam heat exchanger can dramatically deteriorate. Exploring the particle deposition property in the metal foam exchanger becomes crucial. This paper is a numerical investigation aimed to address this issue. Two-dimensional (2D) numerical simulations of a standard one-row tube bundle wrapped with metal foam in cross-flow are performed and highlight preferential particle deposition areas.

A mass-conserving mixed Fourier-Galerkin B-Spline-collocation method for Direct Numerical Simulation of the variable-density Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Reuter, Bryan; Oliver, Todd; Lee, M. K.; Moser, Robert

2017-11-01

We present an algorithm for a Direct Numerical Simulation of the variable-density Navier-Stokes equations based on the velocity-vorticity approach introduced by Kim, Moin, and Moser (1987). In the current work, a Helmholtz decomposition of the momentum is performed. Evolution equations for the curl and the Laplacian of the divergence-free portion are formulated by manipulation of the momentum equations and the curl-free portion is reconstructed by enforcing continuity. The solution is expanded in Fourier bases in the homogeneous directions and B-Spline bases in the inhomogeneous directions. Discrete equations are obtained through a mixed Fourier-Galerkin and collocation weighted residual method. The scheme is designed such that the numerical solution conserves mass locally and globally by ensuring the discrete divergence projection is exact through the use of higher order splines in the inhomogeneous directions. The formulation is tested on multiple variable-density flow problems.

Application of a flux-split algorithm to chemically relaxing, hypervelocity blunt-body flows

NASA Technical Reports Server (NTRS)

Balakrishnan, A.

1987-01-01

Viscous, nonequilibrium, hypervelocity flow fields over two axisymmetric configurations are numerically simulated using a factored, implicit, flux-split algorithm. The governing gas-dynamic and species-continuity equations for laminar flow are presented. The gas-dynamics/nonequilibrium-chemistry coupling procedure is developed as part of the solution procedure and is described in detail. Numerical solutions are presented for hypervelocity flows over a hemisphere and over an axisymmetric aeroassisted orbital transfer vehicle using three different chemistry models. The gas models considered are those for an ideal gas, for a frozen gas, and for chemically relaxing air consisting of five species. The calculated results are compared with existing numerical solutions in the literature along the stagnation line of the hemisphere. The effects of free-stream Reynolds number on the nonequilibrium flow field are discussed.

Knowledge-based simulation for aerospace systems

NASA Technical Reports Server (NTRS)

Will, Ralph W.; Sliwa, Nancy E.; Harrison, F. Wallace, Jr.

1988-01-01

Knowledge-based techniques, which offer many features that are desirable in the simulation and development of aerospace vehicle operations, exhibit many similarities to traditional simulation packages. The eventual solution of these systems' current symbolic processing/numeric processing interface problem will lead to continuous and discrete-event simulation capabilities in a single language, such as TS-PROLOG. Qualitative, totally-symbolic simulation methods are noted to possess several intrinsic characteristics that are especially revelatory of the system being simulated, and capable of insuring that all possible behaviors are considered.

A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Franceschini, Andrea; Ferronato, Massimiliano, E-mail: massimiliano.ferronato@unipd.it; Janna, Carlo

The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion accordingmore » to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.« less

Time-Accurate Local Time Stepping and High-Order Time CESE Methods for Multi-Dimensional Flows Using Unstructured Meshes

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Venkatachari, Balaji Shankar; Cheng, Gary

2013-01-01

With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation

PubMed Central

Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

2014-01-01

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design. PMID:25404761

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

DOE PAGES

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.; ...

2016-09-18

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

magnum.fe: A micromagnetic finite-element simulation code based on FEniCS

NASA Astrophysics Data System (ADS)

Abert, Claas; Exl, Lukas; Bruckner, Florian; Drews, André; Suess, Dieter

2013-11-01

We have developed a finite-element micromagnetic simulation code based on the FEniCS package called magnum.fe. Here we describe the numerical methods that are applied as well as their implementation with FEniCS. We apply a transformation method for the solution of the demagnetization-field problem. A semi-implicit weak formulation is used for the integration of the Landau-Lifshitz-Gilbert equation. Numerical experiments show the validity of simulation results. magnum.fe is open source and well documented. The broad feature range of the FEniCS package makes magnum.fe a good choice for the implementation of novel micromagnetic finite-element algorithms.

Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations

NASA Technical Reports Server (NTRS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Isakov, Sergei V.; Neven, Hartmut; Mazzola, Guglielmo; Troyer, Matthias

2015-01-01

Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

Applying Parallel Adaptive Methods with GeoFEST/PYRAMID to Simulate Earth Surface Crustal Dynamics

NASA Technical Reports Server (NTRS)

Norton, Charles D.; Lyzenga, Greg; Parker, Jay; Glasscoe, Margaret; Donnellan, Andrea; Li, Peggy

2006-01-01

This viewgraph presentation reviews the use Adaptive Mesh Refinement (AMR) in simulating the Crustal Dynamics of Earth's Surface. AMR simultaneously improves solution quality, time to solution, and computer memory requirements when compared to generating/running on a globally fine mesh. The use of AMR in simulating the dynamics of the Earth's Surface is spurred by future proposed NASA missions, such as InSAR for Earth surface deformation and other measurements. These missions will require support for large-scale adaptive numerical methods using AMR to model observations. AMR was chosen because it has been successful in computation fluid dynamics for predictive simulation of complex flows around complex structures.

Time and length scales within a fire and implications for numerical simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

TIESZEN,SHELDON R.

2000-02-02

A partial non-dimensionalization of the Navier-Stokes equations is used to obtain order of magnitude estimates of the rate-controlling transport processes in the reacting portion of a fire plume as a function of length scale. Over continuum length scales, buoyant times scales vary as the square root of the length scale; advection time scales vary as the length scale, and diffusion time scales vary as the square of the length scale. Due to the variation with length scale, each process is dominant over a given range. The relationship of buoyancy and baroclinc vorticity generation is highlighted. For numerical simulation, first principlesmore » solution for fire problems is not possible with foreseeable computational hardware in the near future. Filtered transport equations with subgrid modeling will be required as two to three decades of length scale are captured by solution of discretized conservation equations. By whatever filtering process one employs, one must have humble expectations for the accuracy obtainable by numerical simulation for practical fire problems that contain important multi-physics/multi-length-scale coupling with up to 10 orders of magnitude in length scale.« less

Numerical Simulations For the F-16XL Aircraft Configuration

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa A.; Abdol-Hamid, Khaled; Cavallo, Peter A.; Parlette, Edward B.

2014-01-01

Numerical simulations of flow around the F-16XL are presented as a contribution to the Cranked Arrow Wing Aerodynamic Project International II (CAWAPI-II). The NASA Tetrahedral Unstructured Software System (TetrUSS) is used to perform numerical simulations. This CFD suite, developed and maintained by NASA Langley Research Center, includes an unstructured grid generation program called VGRID, a postprocessor named POSTGRID, and the flow solver USM3D. The CRISP CFD package is utilized to provide error estimates and grid adaption for verification of USM3D results. A subsonic high angle-of-attack case flight condition (FC) 25 is computed and analyzed. Three turbulence models are used in the calculations: the one-equation Spalart-Allmaras (SA), the two-equation shear stress transport (SST) and the ke turbulence models. Computational results, and surface static pressure profiles are presented and compared with flight data. Solution verification is performed using formal grid refinement studies, the solution of Error Transport Equations, and adaptive mesh refinement. The current study shows that the USM3D solver coupled with CRISP CFD can be used in an engineering environment in predicting vortex-flow physics on a complex configuration at flight Reynolds numbers.

Advances in Numerical Boundary Conditions for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.

1997-01-01

Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.

Implicit methods for efficient musculoskeletal simulation and optimal control

PubMed Central

van den Bogert, Antonie J.; Blana, Dimitra; Heinrich, Dieter

2011-01-01

The ordinary differential equations for musculoskeletal dynamics are often numerically stiff and highly nonlinear. Consequently, simulations require small time steps, and optimal control problems are slow to solve and have poor convergence. In this paper, we present an implicit formulation of musculoskeletal dynamics, which leads to new numerical methods for simulation and optimal control, with the expectation that we can mitigate some of these problems. A first order Rosenbrock method was developed for solving forward dynamic problems using the implicit formulation. It was used to perform real-time dynamic simulation of a complex shoulder arm system with extreme dynamic stiffness. Simulations had an RMS error of only 0.11 degrees in joint angles when running at real-time speed. For optimal control of musculoskeletal systems, a direct collocation method was developed for implicitly formulated models. The method was applied to predict gait with a prosthetic foot and ankle. Solutions were obtained in well under one hour of computation time and demonstrated how patients may adapt their gait to compensate for limitations of a specific prosthetic limb design. The optimal control method was also applied to a state estimation problem in sports biomechanics, where forces during skiing were estimated from noisy and incomplete kinematic data. Using a full musculoskeletal dynamics model for state estimation had the additional advantage that forward dynamic simulations, could be done with the same implicitly formulated model to simulate injuries and perturbation responses. While these methods are powerful and allow solution of previously intractable problems, there are still considerable numerical challenges, especially related to the convergence of gradient-based solvers. PMID:22102983

A low-rank control variate for multilevel Monte Carlo simulation of high-dimensional uncertain systems

NASA Astrophysics Data System (ADS)

Fairbanks, Hillary R.; Doostan, Alireza; Ketelsen, Christian; Iaccarino, Gianluca

2017-07-01

Multilevel Monte Carlo (MLMC) is a recently proposed variation of Monte Carlo (MC) simulation that achieves variance reduction by simulating the governing equations on a series of spatial (or temporal) grids with increasing resolution. Instead of directly employing the fine grid solutions, MLMC estimates the expectation of the quantity of interest from the coarsest grid solutions as well as differences between each two consecutive grid solutions. When the differences corresponding to finer grids become smaller, hence less variable, fewer MC realizations of finer grid solutions are needed to compute the difference expectations, thus leading to a reduction in the overall work. This paper presents an extension of MLMC, referred to as multilevel control variates (MLCV), where a low-rank approximation to the solution on each grid, obtained primarily based on coarser grid solutions, is used as a control variate for estimating the expectations involved in MLMC. Cost estimates as well as numerical examples are presented to demonstrate the advantage of this new MLCV approach over the standard MLMC when the solution of interest admits a low-rank approximation and the cost of simulating finer grids grows fast.

Direct Coexistence Methods to Determine the Solubility of Salts in Water from Numerical Simulations. Test Case NaCl.

PubMed

Manzanilla-Granados, Héctor M; Saint-Martín, Humberto; Fuentes-Azcatl, Raúl; Alejandre, José

2015-07-02

The solubility of NaCl, an equilibrium between a saturated solution of ions and a solid with a crystalline structure, was obtained from molecular dynamics simulations using the SPC/E and TIP4P-Ew water models. Four initial setups on supersaturated systems were tested on sodium chloride (NaCl) solutions to determine the equilibrium conditions and computational performance: (1) an ionic solution confined between two crystal plates of periodic NaCl, (2) a solution with all the ions initially distributed randomly, (3) a nanocrystal immersed in pure water, and (4) a nanocrystal immersed in an ionic solution. In some cases, the equilibration of the system can take several microseconds. The results from this work showed that the solubility of NaCl was the same, within simulation error, for the four setups, and in agreement with previously reported values from simulations with the setup (1). The system of a nanocrystal immersed in supersaturated solution was found to equilibrate faster than others. In agreement with laser-Doppler droplet measurements, at equilibrium with the solution the crystals in all the setups had a slight positive charge.

Triangular dislocation: an analytical, artefact-free solution

NASA Astrophysics Data System (ADS)

Nikkhoo, Mehdi; Walter, Thomas R.

2015-05-01

Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

New distributed activation energy model: numerical solution and application to pyrolysis kinetics of some types of biomass.

PubMed

Cai, Junmeng; Liu, Ronghou

2008-05-01

In the present paper, a new distributed activation energy model has been developed, considering the reaction order and the dependence of frequency factor on temperature. The proposed DAEM cannot be solved directly in a closed from, thus a method was used to obtain the numerical solution of the new DAEM equation. Two numerical examples to illustrate the proposed method were presented. The traditional DAEM and new DAEM have been used to simulate the pyrolytic process of some types of biomass. The new DAEM fitted the experimental data much better than the traditional DAEM as the dependence of the frequency factor on temperature was taken into account.

The dynamics of a delayed predator-prey model with state dependent feedback control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Anuraj; Gakkhar, Sunita

2011-11-30

A delayed prey-predator model with state-dependent impulses is investigated. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincare map and analogue of the Poincare Criterion. The qualitative analysis shows that the positive period-one solution bifurcates from the semi-trivial solution through a fold bifurcation. The complex dynamics including chaos is obtained and numerical simulations substantiate the analytical results.

Extraction of gravitational waves in numerical relativity.

PubMed

Bishop, Nigel T; Rezzolla, Luciano

2016-01-01

A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to "extract" the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.

Computer simulation of concentrated solid solution strengthening

NASA Technical Reports Server (NTRS)

Kuo, C. T. K.; Arsenault, R. J.

1976-01-01

The interaction forces between a straight edge dislocation moving through a three-dimensional block containing a random array of solute atoms were determined. The yield stress at 0 K was obtained by determining the average maximum solute-dislocation interaction force that is encountered by edge dislocation, and an expression relating the yield stress to the length of the dislocation and the solute concentration is provided. The magnitude of the solid solution strengthening due to solute atoms can be determined directly from the numerical results, provided the dislocation line length that moves as a unit is specified.

Numerical and Experimental Investigation of Confined Turbulent Multiple Transverse Jets (Briefing Charts)

DTIC Science & Technology

2014-07-29

14.3. The momentum and scalar mixing is investigated through the solution of the Reynolds-Averaged Navier Stokes (RANS) equations. The mean scalar...demonstrated symmetry , only a one-half section of the geometry is considered. All numerical simulations capture salient flow structures such as the counter...distribution unlimited Symmetry Plane Walls Diluents’ Inlet Vy = 100 m/s Previous Numerical Work at AFRL: Air-to-Air Experimental Configuration

A simple analytical infiltration model for short-duration rainfall

NASA Astrophysics Data System (ADS)

Wang, Kaiwen; Yang, Xiaohua; Liu, Xiaomang; Liu, Changming

2017-12-01

Many infiltration models have been proposed to simulate infiltration process. Different initial soil conditions and non-uniform initial water content can lead to infiltration simulation errors, especially for short-duration rainfall (SHR). Few infiltration models are specifically derived to eliminate the errors caused by the complex initial soil conditions. We present a simple analytical infiltration model for SHR infiltration simulation, i.e., Short-duration Infiltration Process model (SHIP model). The infiltration simulated by 5 models (i.e., SHIP (high) model, SHIP (middle) model, SHIP (low) model, Philip model and Parlange model) were compared based on numerical experiments and soil column experiments. In numerical experiments, SHIP (middle) and Parlange models had robust solutions for SHR infiltration simulation of 12 typical soils under different initial soil conditions. The absolute values of percent bias were less than 12% and the values of Nash and Sutcliffe efficiency were greater than 0.83. Additionally, in soil column experiments, infiltration rate fluctuated in a range because of non-uniform initial water content. SHIP (high) and SHIP (low) models can simulate an infiltration range, which successfully covered the fluctuation range of the observed infiltration rate. According to the robustness of solutions and the coverage of fluctuation range of infiltration rate, SHIP model can be integrated into hydrologic models to simulate SHR infiltration process and benefit the flood forecast.

Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics

NASA Astrophysics Data System (ADS)

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

2018-03-01

We investigate three-wave resonant interactions through both the generalized Darboux transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark-dark-soliton formula through the generalized Darboux transformation. Secondly, we use the matrix analysis method to avoid the singularity of transformed potential functions and to find the general nonsingular breather solutions. Moreover, through a limit process, we deduce the general rogue wave solutions and give a classification by their dynamics including bright, dark, four-petals, and two-peaks rogue waves. Ever since the coexistence of dark soliton and rogue wave in non-zero background, their interactions naturally become a quite appealing topic. Based on the N-fold Darboux transformation, we can derive the explicit solutions to depict their interactions. Finally, by performing extensive numerical simulations we can predict whether these dark solitons and rogue waves are stable enough to propagate. These results can be available for several physical subjects such as fluid dynamics, nonlinear optics, solid state physics, and plasma physics.

Permeable Reactive Barriers: Lessons Learned/New Directions

DTIC Science & Technology

2005-02-01

set up to treat simulated mine drainage indicates that the sulfide minerals form in close proximity to the organic solids (Waybrant, Ptacek, and...both vertically and horizontally along the PRB installation area. Groundwater and solute transport modeling can be used to simulate representative...2001; Elder, Benson, and Eykholt 2002). The numerical simulations show that the spatial variations in the hydraulic conductivity of both the aquifer

Geothermal reservoir simulation

NASA Technical Reports Server (NTRS)

Mercer, J. W., Jr.; Faust, C.; Pinder, G. F.

1974-01-01

The prediction of long-term geothermal reservoir performance and the environmental impact of exploiting this resource are two important problems associated with the utilization of geothermal energy for power production. Our research effort addresses these problems through numerical simulation. Computer codes based on the solution of partial-differential equations using finite-element techniques are being prepared to simulate multiphase energy transport, energy transport in fractured porous reservoirs, well bore phenomena, and subsidence.

A perturbation analysis of a mechanical model for stable spatial patterning in embryology

NASA Astrophysics Data System (ADS)

Bentil, D. E.; Murray, J. D.

1992-12-01

We investigate a mechanical cell-traction mechanism that generates stationary spatial patterns. A linear analysis highlights the model's potential for these heterogeneous solutions. We use multiple-scale perturbation techniques to study the evolution of these solutions and compare our solutions with numerical simulations of the model system. We discuss some potential biological applications among which are the formation of ridge patterns, dermatoglyphs, and wound healing.

Towards an Automated Full-Turbofan Engine Numerical Simulation

NASA Technical Reports Server (NTRS)

Reed, John A.; Turner, Mark G.; Norris, Andrew; Veres, Joseph P.

2003-01-01

The objective of this study was to demonstrate the high-fidelity numerical simulation of a modern high-bypass turbofan engine. The simulation utilizes the Numerical Propulsion System Simulation (NPSS) thermodynamic cycle modeling system coupled to a high-fidelity full-engine model represented by a set of coupled three-dimensional computational fluid dynamic (CFD) component models. Boundary conditions from the balanced, steady-state cycle model are used to define component boundary conditions in the full-engine model. Operating characteristics of the three-dimensional component models are integrated into the cycle model via partial performance maps generated automatically from the CFD flow solutions using one-dimensional meanline turbomachinery programs. This paper reports on the progress made towards the full-engine simulation of the GE90-94B engine, highlighting the generation of the high-pressure compressor partial performance map. The ongoing work will provide a system to evaluate the steady and unsteady aerodynamic and mechanical interactions between engine components at design and off-design operating conditions.

Numerical simulation of air hypersonic flows with equilibrium chemical reactions

NASA Astrophysics Data System (ADS)

Emelyanov, Vladislav; Karpenko, Anton; Volkov, Konstantin

2018-05-01

The finite volume method is applied to solve unsteady three-dimensional compressible Navier-Stokes equations on unstructured meshes. High-temperature gas effects altering the aerodynamics of vehicles are taken into account. Possibilities of the use of graphics processor units (GPUs) for the simulation of hypersonic flows are demonstrated. Solutions of some test cases on GPUs are reported, and a comparison between computational results of equilibrium chemically reacting and perfect air flowfields is performed. Speedup of solution on GPUs with respect to the solution on central processor units (CPUs) is compared. The results obtained provide promising perspective for designing a GPU-based software framework for practical applications.

Numerical model for the uptake of groundwater contaminants by phreatophytes

USGS Publications Warehouse

Widdowson, M.A.; El-Sayed, A.; Landmeyer, J.E.

2008-01-01

Conventional solute transport models do not adequately account for the effects of phreatophytic plant systems on contaminant concentrations in shallow groundwater systems. A numerical model was developed and tested to simulate threedimensional reactive solute transport in a heterogeneous porous medium. Advective-dispersive transport is coupled to biodegradation, sorption, and plantbased attenuation processes including plant uptake and sorption by plant roots. The latter effects are a function of the physical-chemical properties of the individual solutes and plant species. Models for plant uptake were tested and evaluated using the experimental data collected at a field site comprised of hybrid poplar trees. A non-linear equilibrium isotherm model best represented site conditions.

Implicit and semi-implicit schemes in the Versatile Advection Code: numerical tests

NASA Astrophysics Data System (ADS)

Toth, G.; Keppens, R.; Botchev, M. A.

1998-04-01

We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with optional source terms. The main advantage of implicit solution strategies over explicit time integration is that the restrictive constraint on the allowed time step can be (partially) eliminated, thus the computational cost is reduced. The test problems cover one and two dimensional, steady state and time accurate computations, and the solutions contain discontinuities. For each test, we confront explicit with implicit solution strategies.

An efficient numerical solution of the transient storage equations for solute transport in small streams

USGS Publications Warehouse

Runkel, Robert L.; Chapra, Steven C.

1993-01-01

Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.

Explicit filtering in large eddy simulation using a discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Brazell, Matthew J.

The discontinuous Galerkin (DG) method is a formulation of the finite element method (FEM). DG provides the ability for a high order of accuracy in complex geometries, and allows for highly efficient parallelization algorithms. These attributes make the DG method attractive for solving the Navier-Stokes equations for large eddy simulation (LES). The main goal of this work is to investigate the feasibility of adopting an explicit filter in the numerical solution of the Navier-Stokes equations with DG. Explicit filtering has been shown to increase the numerical stability of under-resolved simulations and is needed for LES with dynamic sub-grid scale (SGS) models. The explicit filter takes advantage of DG's framework where the solution is approximated using a polyno- mial basis where the higher modes of the solution correspond to a higher order polynomial basis. By removing high order modes, the filtered solution contains low order frequency content much like an explicit low pass filter. The explicit filter implementation is tested on a simple 1-D solver with an initial condi- tion that has some similarity to turbulent flows. The explicit filter does restrict the resolution as well as remove accumulated energy in the higher modes from aliasing. However, the ex- plicit filter is unable to remove numerical errors causing numerical dissipation. A second test case solves the 3-D Navier-Stokes equations of the Taylor-Green vortex flow (TGV). The TGV is useful for SGS model testing because it is initially laminar and transitions into a fully turbulent flow. The SGS models investigated include the constant coefficient Smagorinsky model, dynamic Smagorinsky model, and dynamic Heinz model. The constant coefficient Smagorinsky model is over dissipative, this is generally not desirable however it does add stability. The dynamic Smagorinsky model generally performs better, especially during the laminar-turbulent transition region as expected. The dynamic Heinz model which is based on an improved model, handles the laminar-turbulent transition region well while also showing additional robustness.

Development and testing of a compartmentalized reaction network model for redox zones in contaminated aquifers

USGS Publications Warehouse

Abrams , Robert H.; Loague, Keith; Kent, Douglas B.

1998-01-01

The work reported here is the first part of a larger effort focused on efficient numerical simulation of redox zone development in contaminated aquifers. The sequential use of various electron acceptors, which is governed by the energy yield of each reaction, gives rise to redox zones. The large difference in energy yields between the various redox reactions leads to systems of equations that are extremely ill-conditioned. These equations are very difficult to solve, especially in the context of coupled fluid flow, solute transport, and geochemical simulations. We have developed a general, rational method to solve such systems where we focus on the dominant reactions, compartmentalizing them in a manner that is analogous to the redox zones that are often observed in the field. The compartmentalized approach allows us to easily solve a complex geochemical system as a function of time and energy yield, laying the foundation for our ongoing work in which we couple the reaction network, for the development of redox zones, to a model of subsurface fluid flow and solute transport. Our method (1) solves the numerical system without evoking a redox parameter, (2) improves the numerical stability of redox systems by choosing which compartment and thus which reaction network to use based upon the concentration ratios of key constituents, (3) simulates the development of redox zones as a function of time without the use of inhibition factors or switching functions, and (4) can reduce the number of transport equations that need to be solved in space and time. We show through the use of various model performance evaluation statistics that the appropriate compartment choice under different geochemical conditions leads to numerical solutions without significant error. The compartmentalized approach described here facilitates the next phase of this effort where we couple the redox zone reaction network to models of fluid flow and solute transport.

Numerical Modeling of Solidification in Space With MEPHISTO-4. Part 2

NASA Technical Reports Server (NTRS)

Simpson, James E.; Yoa, Minwu; deGroh, Henry C., III; Garimella, V. Suresh

1998-01-01

A pre-flight analysis of the directional solidification of BiSn with MEPHISTO-4 is presented. Simplified Bridgman growth under microgravity conditions is simulated using a two dimensional finite element model. This numerical model is a single domain, pseudo-steady state model, and includes the effects of both thermal and solutal convection. The results show that for all orientations of the applied steady state gravity vector, of magnitude 1 micro-g, the directional solidification process remains diffusion controlled. The maximum convective velocity was found to be 4.424 x 10(exp -5) cm/s for the horizontal Bridgman growth configuration. This value is an order of magnitude lower than the growth velocity. The maximum and minimum values or solute concentration in the liquid at the crystal-melt interface were 13.867 at.% and 13.722 at.%, respectively. This gives a radial segregation value of xi = 1.046% at the interface. A secondary objective of this work was to compare the results obtained to those that consider thermal convection only (no solutal convection). It was found that the convective flow patterns in simulations which included solutal convection were significantly different from those which ignored solutal convection. The level of radial segregation predicted by the current simulations is an order of magnitude lower than that found in simulations which ignore solutal convection. The final aim was to investigate the effect of g-jitter on the crystal growth process. A simulation was performed to calculate the system response to a 1 second, 100 micro-g gravity impulse acting normal to the direction of growth. This pulse is consistent with that induced by Orbiter thruster firings. The results obtained indicate that such a gravity pulse causes an increase in the level of radial solute segregation at the interface from the steady state values. The maximum value of solute concentration in the liquid was found to be 13.888 at.%, the minimum value calculated was 13.706 at.%, yielding a radial segregation value of xi = 1.31% at the interface. These values occurred 126 seconds after the pulse terminated. Thus it is anticipated that the process will remain diffusion controlled even when subjected to such g-jitter.

The Effect of Basis Selection on Thermal-Acoustic Random Response Prediction Using Nonlinear Modal Simulation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2004-01-01

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermal-acoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii - iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime.

Numerical Simulation of Delamination Growth in Composite Materials

NASA Technical Reports Server (NTRS)

Camanho, P. P.; Davila, C. G.; Ambur, D. R.

2001-01-01

The use of decohesion elements for the simulation of delamination in composite materials is reviewed. The test methods available to measure the interfacial fracture toughness used in the formulation of decohesion elements are described initially. After a brief presentation of the virtual crack closure technique, the technique most widely used to simulate delamination growth, the formulation of interfacial decohesion elements is described. Problems related with decohesion element constitutive equations, mixed-mode crack growth, element numerical integration and solution procedures are discussed. Based on these investigations, it is concluded that the use of interfacial decohesion elements is a promising technique that avoids the need for a pre-existing crack and pre-defined crack paths, and that these elements can be used to simulate both delamination onset and growth.

Modeling mass transfer and reaction of dilute solutes in a ternary phase system by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Fu, Yu-Hang; Bai, Lin; Luo, Kai-Hong; Jin, Yong; Cheng, Yi

2017-04-01

In this work, we propose a general approach for modeling mass transfer and reaction of dilute solute(s) in incompressible three-phase flows by introducing a collision operator in lattice Boltzmann (LB) method. An LB equation was used to simulate the solute dynamics among three different fluids, in which the newly expanded collision operator was used to depict the interface behavior of dilute solute(s). The multiscale analysis showed that the presented model can recover the macroscopic transport equations derived from the Maxwell-Stefan equation for dilute solutes in three-phase systems. Compared with the analytical equation of state of solute and dynamic behavior, these results are proven to constitute a generalized framework to simulate solute distributions in three-phase flows, including compound soluble in one phase, compound adsorbed on single-interface, compound in two phases, and solute soluble in three phases. Moreover, numerical simulations of benchmark cases, such as phase decomposition, multilayered planar interfaces, and liquid lens, were performed to test the stability and efficiency of the model. Finally, the multiphase mass transfer and reaction in Janus droplet transport in a straight microchannel were well reproduced.

Reduced-Order Direct Numerical Simulation of Solute Transport in Porous Media

NASA Astrophysics Data System (ADS)

Mehmani, Yashar; Tchelepi, Hamdi

2017-11-01

Pore-scale models are an important tool for analyzing fluid dynamics in porous materials (e.g., rocks, soils, fuel cells). Current direct numerical simulation (DNS) techniques, while very accurate, are computationally prohibitive for sample sizes that are statistically representative of the porous structure. Reduced-order approaches such as pore-network models (PNM) aim to approximate the pore-space geometry and physics to remedy this problem. Predictions from current techniques, however, have not always been successful. This work focuses on single-phase transport of a passive solute under advection-dominated regimes and delineates the minimum set of approximations that consistently produce accurate PNM predictions. Novel network extraction (discretization) and particle simulation techniques are developed and compared to high-fidelity DNS simulations for a wide range of micromodel heterogeneities and a single sphere pack. Moreover, common modeling assumptions in the literature are analyzed and shown that they can lead to first-order errors under advection-dominated regimes. This work has implications for optimizing material design and operations in manufactured (electrodes) and natural (rocks) porous media pertaining to energy systems. This work was supported by the Stanford University Petroleum Research Institute for Reservoir Simulation (SUPRI-B).

ParaExp Using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations

NASA Astrophysics Data System (ADS)

Merkel, M.; Niyonzima, I.; Schöps, S.

2017-12-01

Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into subintervals and computes the solution on each subinterval in parallel. The overall solution is decomposed into a particular solution defined on each subinterval with zero initial conditions and a homogeneous solution propagated by the matrix exponential applied to the initial conditions. The efficiency of the method depends on fast approximations of this matrix exponential based on recent results from numerical linear algebra. This paper deals with the application of ParaExp in combination with Leapfrog to electromagnetic wave problems in time domain. Numerical tests are carried out for a simple toy problem and a realistic spiral inductor model discretized by the Finite Integration Technique.

High-Order Methods for Incompressible Fluid Flow

NASA Astrophysics Data System (ADS)

Deville, M. O.; Fischer, P. F.; Mund, E. H.

2002-08-01

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications.

A Numerical Simulation of Scattering from One-Dimensional Inhomogeneous Dielectric Random Surfaces

NASA Technical Reports Server (NTRS)

Sarabandi, Kamal; Oh, Yisok; Ulaby, Fawwaz T.

1996-01-01

In this paper, an efficient numerical solution for the scattering problem of inhomogeneous dielectric rough surfaces is presented. The inhomogeneous dielectric random surface represents a bare soil surface and is considered to be comprised of a large number of randomly positioned dielectric humps of different sizes, shapes, and dielectric constants above an impedance surface. Clods with nonuniform moisture content and rocks are modeled by inhomogeneous dielectric humps and the underlying smooth wet soil surface is modeled by an impedance surface. In this technique, an efficient numerical solution for the constituent dielectric humps over an impedance surface is obtained using Green's function derived by the exact image theory in conjunction with the method of moments. The scattered field from a sample of the rough surface is obtained by summing the scattered fields from all the individual humps of the surface coherently ignoring the effect of multiple scattering between the humps. The statistical behavior of the scattering coefficient sigma(sup 0) is obtained from the calculation of scattered fields of many different realizations of the surface. Numerical results are presented for several different roughnesses and dielectric constants of the random surfaces. The numerical technique is verified by comparing the numerical solution with the solution based on the small perturbation method and the physical optics model for homogeneous rough surfaces. This technique can be used to study the behavior of scattering coefficient and phase difference statistics of rough soil surfaces for which no analytical solution exists.

LASER APPLICATIONS IN MEDICINE: Effect of glucose concentration in a model light-scattering suspension on propagation of ultrashort laser pulses

NASA Astrophysics Data System (ADS)

Popov, A. P.; Priezzhev, A. V.; Myllylä, Risto

2005-11-01

The propagation of laser pulses in the 2% aqueous solution of intralipid — a suspension of lipid particles with optical properties close to those of the human skin, is numerically simulated at different glucose concentrations. The temporal profiles of 820-nm laser pulses diffusely backscattered from a flat, 2-mm thick solution layer are simulated. The laser pulse profiles are detected by fibreoptic detectors of diameter 0.3 mm with the numerical apertures 0.19, 0.29, and 0.39. It is shown that this method can be used to detect changes in the glucose level in the physiological concentration range (100-500 mg dL-1) by monitoring variations in the peak intensity and area of the laser pulse temporal profile (pulse energy).

Vortex breakdown simulation

NASA Technical Reports Server (NTRS)

Hafez, M.; Ahmad, J.; Kuruvila, G.; Salas, M. D.

1987-01-01

In this paper, steady, axisymmetric inviscid, and viscous (laminar) swirling flows representing vortex breakdown phenomena are simulated using a stream function-vorticity-circulation formulation and two numerical methods. The first is based on an inverse iteration, where a norm of the solution is prescribed and the swirling parameter is calculated as a part of the output. The second is based on direct Newton iterations, where the linearized equations, for all the unknowns, are solved simultaneously by an efficient banded Gaussian elimination procedure. Several numerical solutions for inviscid and viscous flows are demonstrated, followed by a discussion of the results. Some improvements on previous work have been achieved: first order upwind differences are replaced by second order schemes, line relaxation procedure (with linear convergence rate) is replaced by Newton's iterations (which converge quadratically), and Reynolds numbers are extended from 200 up to 1000.

Suboptimal Scheduling in Switched Systems With Continuous-Time Dynamics: A Least Squares Approach.

PubMed

Sardarmehni, Tohid; Heydari, Ali

2018-06-01

Two approximate solutions for optimal control of switched systems with autonomous subsystems and continuous-time dynamics are presented. The first solution formulates a policy iteration (PI) algorithm for the switched systems with recursive least squares. To reduce the computational burden imposed by the PI algorithm, a second solution, called single loop PI, is presented. Online and concurrent training algorithms are discussed for implementing each solution. At last, effectiveness of the presented algorithms is evaluated through numerical simulations.

A Dynamic Eddy Viscosity Model for the Shallow Water Equations Solved by Spectral Element and Discontinuous Galerkin Methods

NASA Astrophysics Data System (ADS)

Marras, Simone; Suckale, Jenny; Giraldo, Francis X.; Constantinescu, Emil

2016-04-01

We present the solution of the viscous shallow water equations where viscosity is built as a residual-based subgrid scale model originally designed for large eddy simulation of compressible [1] and stratified flows [2]. The necessity of viscosity for a shallow water model not only finds motivation from mathematical analysis [3], but is supported by physical reasoning as can be seen by an analysis of the energetics of the solution. We simulated the flow of an idealized wave as it hits a set of obstacles. The kinetic energy spectrum of this flow shows that, although the inviscid Galerkin solutions -by spectral elements and discontinuous Galerkin [4]- preserve numerical stability in spite of the spurious oscillations in the proximity of the wave fronts, the slope of the energy cascade deviates from the theoretically expected values. We show that only a sufficiently small amount of dynamically adaptive viscosity removes the unwanted high-frequency modes while preserving the overall sharpness of the solution. In addition, it yields a physically plausible energy decay. This work is motivated by a larger interest in the application of a shallow water model to the solution of tsunami triggered coastal flows. In particular, coastal flows in regions around the world where coastal parks made of mitigation hills of different sizes and configurations are considered as a means to deviate the power of the incoming wave. References [1] M. Nazarov and J. Hoffman (2013) "Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods" Int. J. Numer. Methods Fluids, 71:339-357 [2] S. Marras, M. Nazarov, F. X. Giraldo (2015) "Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES" J. Comput. Phys. 301:77-101 [3] J. F. Gerbeau and B. Perthame (2001) "Derivation of the viscous Saint-Venant system for laminar shallow water; numerical validation" Discrete Contin. Dyn. Syst. Ser. B, 1:89?102 [4] F. X. Giraldo and M. Restelli (2010) "High-order semi-implicit time-integrators for a triangular discontinuous Galerkin oceanic shallow water model. Int. J. Numer. Methods Fluids, 63:1077-1102

Aggregation work at polydisperse micellization: ideal solution and "dressed micelle" models comparing to molecular dynamics simulations.

PubMed

Burov, S V; Shchekin, A K

2010-12-28

General thermodynamic relations for the work of polydisperse micelle formation in the model of ideal solution of molecular aggregates in nonionic surfactant solution and the model of "dressed micelles" in ionic solution have been considered. In particular, the dependence of the aggregation work on the total concentration of nonionic surfactant has been analyzed. The analogous dependence for the work of formation of ionic aggregates has been examined with regard to existence of two variables of a state of an ionic aggregate, the aggregation numbers of surface active ions and counterions. To verify the thermodynamic models, the molecular dynamics simulations of micellization in nonionic and ionic surfactant solutions at two total surfactant concentrations have been performed. It was shown that for nonionic surfactants, even at relatively high total surfactant concentrations, the shape and behavior of the work of polydisperse micelle formation found within the model of the ideal solution at different total surfactant concentrations agrees fairly well with the numerical experiment. For ionic surfactant solutions, the numerical results indicate a strong screening of ionic aggregates by the bound counterions. This fact as well as independence of the coefficient in the law of mass action for ionic aggregates on total surfactant concentration and predictable behavior of the "waterfall" lines of surfaces of the aggregation work upholds the model of "dressed" ionic aggregates.

ROTATING ACCRETION FLOWS: FROM INFINITY TO THE BLACK HOLE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Jason; Ostriker, Jeremiah; Sunyaev, Rashid, E-mail: jgli@astro.princeton.edu

2013-04-20

Accretion onto a supermassive black hole of a rotating inflow is a particularly difficult problem to study because of the wide range of length scales involved. There have been broadly utilized analytic and numerical treatments of the global properties of accretion flows, but detailed numerical simulations are required to address certain critical aspects. We use the ZEUS code to run hydrodynamical simulations of rotating, axisymmetric accretion flows with Bremsstrahlung cooling, considering solutions for which the centrifugal balance radius significantly exceeds the Schwarzschild radius, with and without viscous angular momentum transport. Infalling gas is followed from well beyond the Bondi radiusmore » down to the vicinity of the black hole. We produce a continuum of solutions with respect to the single parameter M-dot{sub B}/ M-dot{sub Edd}, and there is a sharp transition between two general classes of solutions at an Eddington ratio of M-dot{sub B}/M-dot{sub Edd}{approx}few Multiplication-Sign 10{sup -2}. Our high inflow solutions are very similar to the standard Shakura and Sunyaev results. But our low inflow results are to zeroth order the stationary Papaloizou and Pringle solution, which has no accretion. To next order in the small, assumed viscosity they show circulation, with disk and conical wind outflows almost balancing inflow. These solutions are characterized by hot, vertically extended disks, and net accretion proceeds at an extremely low rate, only of order {alpha} times the inflow rate. Our simulations have converged with respect to spatial resolution and temporal duration, and they do not depend strongly on our choice of boundary conditions.« less

A texture-based framework for improving CFD data visualization in a virtual environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bivins, Gerrick O'Ron

2005-01-01

In the field of computational fluid dynamics (CFD) accurate representations of fluid phenomena can be simulated hut require large amounts of data to represent the flow domain. Most datasets generated from a CFD simulation can be coarse, ~10,000 nodes or cells, or very fine with node counts on the order of 1,000,000. A typical dataset solution can also contain multiple solutions for each node, pertaining to various properties of the flow at a particular node. Scalar properties such as density, temperature, pressure, and velocity magnitude are properties that are typically calculated and stored in a dataset solution. Solutions are notmore » limited to just scalar properties. Vector quantities, such as velocity, are also often calculated and stored for a CFD simulation. Accessing all of this data efficiently during runtime is a key problem for visualization in an interactive application. Understanding simulation solutions requires a post-processing tool to convert the data into something more meaningful. Ideally, the application would present an interactive visual representation of the numerical data for any dataset that was simulated while maintaining the accuracy of the calculated solution. Most CFD applications currently sacrifice interactivity for accuracy, yielding highly detailed flow descriptions hut limiting interaction for investigating the field.« less

A texture-based frameowrk for improving CFD data visualization in a virtual environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bivins, Gerrick O'Ron

2005-01-01

In the field of computational fluid dynamics (CFD) accurate representations of fluid phenomena can be simulated but require large amounts of data to represent the flow domain. Most datasets generated from a CFD simulation can be coarse, ~ 10,000 nodes or cells, or very fine with node counts on the order of 1,000,000. A typical dataset solution can also contain multiple solutions for each node, pertaining to various properties of the flow at a particular node. Scalar properties such as density, temperature, pressure, and velocity magnitude are properties that are typically calculated and stored in a dataset solution. Solutions aremore » not limited to just scalar properties. Vector quantities, such as velocity, are also often calculated and stored for a CFD simulation. Accessing all of this data efficiently during runtime is a key problem for visualization in an interactive application. Understanding simulation solutions requires a post-processing tool to convert the data into something more meaningful. Ideally, the application would present an interactive visual representation of the numerical data for any dataset that was simulated while maintaining the accuracy of the calculated solution. Most CFD applications currently sacrifice interactivity for accuracy, yielding highly detailed flow descriptions but limiting interaction for investigating the field.« less

Fluid Flow and Solidification Under Combined Action of Magnetic Fields and Microgravity

NASA Technical Reports Server (NTRS)

Li, B. Q.; Shu, Y.; Li, K.; deGroh, H. C.

2002-01-01

Mathematical models, both 2-D and 3-D, are developed to represent g-jitter induced fluid flows and their effects on solidification under combined action of magnetic fields and microgravity. The numerical model development is based on the finite element solution of governing equations describing the transient g-jitter driven fluid flows, heat transfer and solutal transport during crystal growth with and without an applied magnetic field in space vehicles. To validate the model predictions, a ground-based g-jitter simulator is developed using the oscillating wall temperatures where timely oscillating fluid flows are measured using a laser PIV system. The measurements are compared well with numerical results obtained from the numerical models. Results show that a combined action derived from magnetic damping and microgravity can be an effective means to control the melt flow and solutal transport in space single crystal growth systems.

Numerics and subgrid-scale modeling in large eddy simulations of stratocumulus clouds.

PubMed

Pressel, Kyle G; Mishra, Siddhartha; Schneider, Tapio; Kaul, Colleen M; Tan, Zhihong

2017-06-01

Stratocumulus clouds are the most common type of boundary layer cloud; their radiative effects strongly modulate climate. Large eddy simulations (LES) of stratocumulus clouds often struggle to maintain fidelity to observations because of the sharp gradients occurring at the entrainment interfacial layer at the cloud top. The challenge posed to LES by stratocumulus clouds is evident in the wide range of solutions found in the LES intercomparison based on the DYCOMS-II field campaign, where simulated liquid water paths for identical initial and boundary conditions varied by a factor of nearly 12. Here we revisit the DYCOMS-II RF01 case and show that the wide range of previous LES results can be realized in a single LES code by varying only the numerical treatment of the equations of motion and the nature of subgrid-scale (SGS) closures. The simulations that maintain the greatest fidelity to DYCOMS-II observations are identified. The results show that using weighted essentially non-oscillatory (WENO) numerics for all resolved advective terms and no explicit SGS closure consistently produces the highest-fidelity simulations. This suggests that the numerical dissipation inherent in WENO schemes functions as a high-quality, implicit SGS closure for this stratocumulus case. Conversely, using oscillatory centered difference numerical schemes for momentum advection, WENO numerics for scalars, and explicitly modeled SGS fluxes consistently produces the lowest-fidelity simulations. We attribute this to the production of anomalously large SGS fluxes near the cloud tops through the interaction of numerical error in the momentum field with the scalar SGS model.

Numerics and subgrid‐scale modeling in large eddy simulations of stratocumulus clouds

PubMed Central

Mishra, Siddhartha; Schneider, Tapio; Kaul, Colleen M.; Tan, Zhihong

2017-01-01

Abstract Stratocumulus clouds are the most common type of boundary layer cloud; their radiative effects strongly modulate climate. Large eddy simulations (LES) of stratocumulus clouds often struggle to maintain fidelity to observations because of the sharp gradients occurring at the entrainment interfacial layer at the cloud top. The challenge posed to LES by stratocumulus clouds is evident in the wide range of solutions found in the LES intercomparison based on the DYCOMS‐II field campaign, where simulated liquid water paths for identical initial and boundary conditions varied by a factor of nearly 12. Here we revisit the DYCOMS‐II RF01 case and show that the wide range of previous LES results can be realized in a single LES code by varying only the numerical treatment of the equations of motion and the nature of subgrid‐scale (SGS) closures. The simulations that maintain the greatest fidelity to DYCOMS‐II observations are identified. The results show that using weighted essentially non‐oscillatory (WENO) numerics for all resolved advective terms and no explicit SGS closure consistently produces the highest‐fidelity simulations. This suggests that the numerical dissipation inherent in WENO schemes functions as a high‐quality, implicit SGS closure for this stratocumulus case. Conversely, using oscillatory centered difference numerical schemes for momentum advection, WENO numerics for scalars, and explicitly modeled SGS fluxes consistently produces the lowest‐fidelity simulations. We attribute this to the production of anomalously large SGS fluxes near the cloud tops through the interaction of numerical error in the momentum field with the scalar SGS model. PMID:28943997

Curvilinear immersed-boundary method for simulating unsteady flows in shallow natural streams with arbitrarily complex obstacles

NASA Astrophysics Data System (ADS)

Kang, Seokkoo; Borazjani, Iman; Sotiropoulos, Fotis

2008-11-01

Unsteady 3D simulations of flows in natural streams is a challenging task due to the complexity of the bathymetry, the shallowness of the flow, and the presence of multiple nature- and man-made obstacles. This work is motivated by the need to develop a powerful numerical method for simulating such flows using coherent-structure-resolving turbulence models. We employ the curvilinear immersed boundary method of Ge and Sotiropoulos (Journal of Computational Physics, 2007) and address the critical issue of numerical efficiency in large aspect ratio computational domains and grids such as those encountered in long and shallow open channels. We show that the matrix-free Newton-Krylov method for solving the momentum equations coupled with an algebraic multigrid method with incomplete LU preconditioner for solving the Poisson equation yield a robust and efficient procedure for obtaining time-accurate solutions in such problems. We demonstrate the potential of the numerical approach by carrying out a direct numerical simulation of flow in a long and shallow meandering stream with multiple hydraulic structures.

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) for Breast Tumor Imaging: Numerical Modeling and Simulation

PubMed Central

Zhou, Lian; Li, Xu; Zhu, Shanan; He, Bin

2011-01-01

Magnetoacoustic tomography with magnetic induction (MAT-MI) was recently introduced as a noninvasive electrical conductivity imaging approach with high spatial resolution close to ultrasound imaging. In the present study, we test the feasibility of the MAT-MI method for breast tumor imaging using numerical modeling and computer simulation. Using the finite element method, we have built three dimensional numerical breast models with varieties of embedded tumors for this simulation study. In order to obtain an accurate and stable forward solution that does not have numerical errors caused by singular MAT-MI acoustic sources at conductivity boundaries, we first derive an integral forward method for calculating MAT-MI acoustic sources over the entire imaging volume. An inverse algorithm for reconstructing the MAT-MI acoustic source is also derived with spherical measurement aperture, which simulates a practical setup for breast imaging. With the numerical breast models, we have conducted computer simulations under different imaging parameter setups and all the results suggest that breast tumors that have large conductivity contrast to its surrounding tissues as reported in literature may be readily detected in the reconstructed MAT-MI images. In addition, our simulations also suggest that the sensitivity of imaging breast tumors using the presented MAT-MI setup depends more on the tumor location and the conductivity contrast between the tumor and its surrounding tissues than on the tumor size. PMID:21364262

Numerical and experimental approaches to simulate soil clogging in porous media

NASA Astrophysics Data System (ADS)

Kanarska, Yuliya; LLNL Team

2012-11-01

Failure of a dam by erosion ranks among the most serious accidents in civil engineering. The best way to prevent internal erosion is using adequate granular filters in the transition areas where important hydraulic gradients can appear. In case of cracking and erosion, if the filter is capable of retaining the eroded particles, the crack will seal and the dam safety will be ensured. A finite element numerical solution of the Navier-Stokes equations for fluid flow together with Lagrange multiplier technique for solid particles was applied to the simulation of soil filtration. The numerical approach was validated through comparison of numerical simulations with the experimental results of base soil particle clogging in the filter layers performed at ERDC. The numerical simulation correctly predicted flow and pressure decay due to particle clogging. The base soil particle distribution was almost identical to those measured in the laboratory experiment. To get more precise understanding of the soil transport in granular filters we investigated sensitivity of particle clogging mechanisms to various aspects such as particle size ration, the amplitude of hydraulic gradient, particle concentration and contact properties. By averaging the results derived from the grain-scale simulations, we investigated how those factors affect the semi-empirical multiphase model parameters in the large-scale simulation tool. The Department of Homeland Security Science and Technology Directorate provided funding for this research.

Multi-Scale Fusion of Information for Uncertainty Quantification and Management in Large-Scale Simulations

DTIC Science & Technology

2015-12-02

simplification of the equations but at the expense of introducing modeling errors. We have shown that the Wick solutions have accuracy comparable to...the system of equations for the coefficients of formal power series solutions . Moreover, the structure of this propagator is seemingly universal, i.e...the problem of computing the numerical solution to kinetic partial differential equa- tions involving many phase variables. These types of equations

Fluid Dynamics of Carbon Dioxide Disposal into Saline Aquifers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, Julio Enrique

2003-01-01

Injection of carbon dioxide (CO 2) into saline aquifers has been proposed as a means to reduce greenhouse gas emissions (geological carbon sequestration). Large-scale injection of CO 2 will induce a variety of coupled physical and chemical processes, including multiphase fluid flow, fluid pressurization and changes in effective stress, solute transport, and chemical reactions between fluids and formation minerals. This work addresses some of these issues with special emphasis given to the physics of fluid flow in brine formations. An investigation of the thermophysical properties of pure carbon dioxide, water and aqueous solutions of CO 2 and NaCl has beenmore » conducted. As a result, accurate representations and models for predicting the overall thermophysical behavior of the system CO 2-H 2O-NaCl are proposed and incorporated into the numerical simulator TOUGH2/ECO2. The basic problem of CO 2 injection into a radially symmetric brine aquifer is used to validate the results of TOUGH2/ECO2. The numerical simulator has been applied to more complex flow problem including the CO 2 injection project at the Sleipner Vest Field in the Norwegian sector of the North Sea and the evaluation of fluid flow dynamics effects of CO 2 injection into aquifers. Numerical simulation results show that the transport at Sleipner is dominated by buoyancy effects and that shale layers control vertical migration of CO 2. These results are in good qualitative agreement with time lapse surveys performed at the site. High-resolution numerical simulation experiments have been conducted to study the onset of instabilities (viscous fingering) during injection of CO 2 into saline aquifers. The injection process can be classified as immiscible displacement of an aqueous phase by a less dense and less viscous gas phase. Under disposal conditions (supercritical CO 2) the viscosity of carbon dioxide can be less than the viscosity of the aqueous phase by a factor of 15. Because of the lower viscosity, the CO 2 displacement front will have a tendency towards instability. Preliminary simulation results show good agreement between classical instability solutions and numerical predictions of finger growth and spacing obtained using different gas/liquid viscosity ratios, relative permeability and capillary pressure models. Further studies are recommended to validate these results over a broader range of conditions.« less

acme: The Amendable Coal-Fire Modeling Exercise. A C++ Class Library for the Numerical Simulation of Coal-Fires

NASA Astrophysics Data System (ADS)

Wuttke, Manfred W.

2017-04-01

At LIAG, we use numerical models to develop and enhance understanding of coupled transport processes and to predict the dynamics of the system under consideration. Topics include geothermal heat utilization, subrosion processes, and spontaneous underground coal fires. Although the details make it inconvenient if not impossible to apply a single code implementation to all systems, their investigations go along similar paths: They all depend on the solution of coupled transport equations. We thus saw a need for a modular code system with open access for the various communities to maximize the shared synergistic effects. To this purpose we develop the oops! ( open object-oriented parallel solutions) - toolkit, a C++ class library for the numerical solution of mathematical models of coupled thermal, hydraulic and chemical processes. This is used to develop problem-specific libraries like acme( amendable coal-fire modeling exercise), a class library for the numerical simulation of coal-fires and applications like kobra (Kohlebrand, german for coal-fire), a numerical simulation code for standard coal-fire models. Basic principle of the oops!-code system is the provision of data types for the description of space and time dependent data fields, description of terms of partial differential equations (pde), their discretisation and solving methods. Coupling of different processes, described by their particular pde is modeled by an automatic timescale-ordered operator-splitting technique. acme is a derived coal-fire specific application library, depending on oops!. If specific functionalities of general interest are implemented and have been tested they will be assimilated into the main oops!-library. Interfaces to external pre- and post-processing tools are easily implemented. Thus a construction kit which can be arbitrarily amended is formed. With the kobra-application constructed with acme we study the processes and propagation of shallow coal seam fires in particular in Xinjiang, China, as well as analyze and interpret results from lab experiments.

A validated non-linear Kelvin-Helmholtz benchmark for numerical hydrodynamics

NASA Astrophysics Data System (ADS)

Lecoanet, D.; McCourt, M.; Quataert, E.; Burns, K. J.; Vasil, G. M.; Oishi, J. S.; Brown, B. P.; Stone, J. M.; O'Leary, R. M.

2016-02-01

The non-linear evolution of the Kelvin-Helmholtz instability is a popular test for code verification. To date, most Kelvin-Helmholtz problems discussed in the literature are ill-posed: they do not converge to any single solution with increasing resolution. This precludes comparisons among different codes and severely limits the utility of the Kelvin-Helmholtz instability as a test problem. The lack of a reference solution has led various authors to assert the accuracy of their simulations based on ad hoc proxies, e.g. the existence of small-scale structures. This paper proposes well-posed two-dimensional Kelvin-Helmholtz problems with smooth initial conditions and explicit diffusion. We show that in many cases numerical errors/noise can seed spurious small-scale structure in Kelvin-Helmholtz problems. We demonstrate convergence to a reference solution using both ATHENA, a Godunov code, and DEDALUS, a pseudo-spectral code. Problems with constant initial density throughout the domain are relatively straightforward for both codes. However, problems with an initial density jump (which are the norm in astrophysical systems) exhibit rich behaviour and are more computationally challenging. In the latter case, ATHENA simulations are prone to an instability of the inner rolled-up vortex; this instability is seeded by grid-scale errors introduced by the algorithm, and disappears as resolution increases. Both ATHENA and DEDALUS exhibit late-time chaos. Inviscid simulations are riddled with extremely vigorous secondary instabilities which induce more mixing than simulations with explicit diffusion. Our results highlight the importance of running well-posed test problems with demonstrated convergence to a reference solution. To facilitate future comparisons, we include as supplementary material the resolved, converged solutions to the Kelvin-Helmholtz problems in this paper in machine-readable form.

Direction dependence of displacement time for two-fluid electroosmotic flow.

PubMed

Lim, Chun Yee; Lam, Yee Cheong

2012-03-01

Electroosmotic flow that involves one fluid displacing another fluid is commonly encountered in various microfludic applications and experiments, for example, current monitoring technique to determine zeta potential of microchannel. There is experimentally observed anomaly in such flow, namely, the displacement time is flow direction dependent, i.e., it depends if it is a high concentration fluid displacing a low concentration fluid, or vice versa. Thus, this investigation focuses on the displacement flow of two fluids with various concentration differences. The displacement time was determined experimentally with current monitoring method. It is concluded that the time required for a high concentration solution to displace a low concentration solution is smaller than the time required for a low concentration solution to displace a high concentration solution. The percentage displacement time difference increases with increasing concentration difference and independent of the length or width of the channel and the voltage applied. Hitherto, no theoretical analysis or numerical simulation has been conducted to explain this phenomenon. A numerical model based on finite element method was developed to explain the experimental observations. Simulations showed that the velocity profile and ion distribution deviate significantly from a single fluid electroosmotic flow. The distortion of ion distribution near the electrical double layer is responsible for the displacement time difference for the two different flow directions. The trends obtained from simulations agree with the experimental findings.

Direction dependence of displacement time for two-fluid electroosmotic flow

PubMed Central

Lim, Chun Yee; Lam, Yee Cheong

2012-01-01

Electroosmotic flow that involves one fluid displacing another fluid is commonly encountered in various microfludic applications and experiments, for example, current monitoring technique to determine zeta potential of microchannel. There is experimentally observed anomaly in such flow, namely, the displacement time is flow direction dependent, i.e., it depends if it is a high concentration fluid displacing a low concentration fluid, or vice versa. Thus, this investigation focuses on the displacement flow of two fluids with various concentration differences. The displacement time was determined experimentally with current monitoring method. It is concluded that the time required for a high concentration solution to displace a low concentration solution is smaller than the time required for a low concentration solution to displace a high concentration solution. The percentage displacement time difference increases with increasing concentration difference and independent of the length or width of the channel and the voltage applied. Hitherto, no theoretical analysis or numerical simulation has been conducted to explain this phenomenon. A numerical model based on finite element method was developed to explain the experimental observations. Simulations showed that the velocity profile and ion distribution deviate significantly from a single fluid electroosmotic flow. The distortion of ion distribution near the electrical double layer is responsible for the displacement time difference for the two different flow directions. The trends obtained from simulations agree with the experimental findings. PMID:22662083

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

NASA Astrophysics Data System (ADS)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

Dispersive models describing mosquitoes’ population dynamics

NASA Astrophysics Data System (ADS)

Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.

2016-08-01

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

Numeric Solutions of Dirac-Gursey Spinor Field Equation Under External Gaussian White Noise

NASA Astrophysics Data System (ADS)

Aydogmus, Fatma

2016-06-01

In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.

Analytical formulation of selected activities of the remote manipulator system

NASA Technical Reports Server (NTRS)

Zimmerman, K. J.

1977-01-01

Existing analysis of Orbiter-RMS-Payload kinematics were surveyed, including equations dealing with the two body kinematics in the presence of a massless RMS and compares analytical explicit solutions with numerical solutions. For the following operational phases of the RMS numerical demonstration, problems are provided: (1) payload capture; (2) payload stowage and removal from cargo bay; and (3) payload deployment. The equation of motion provided accounted for RMS control forces and torque moments and could be extended to RMS flexibility and control loop simulation without increasing the degrees of freedom of the two body system.

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations.

PubMed

Lue, Leo; Linse, Per

2011-12-14

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion. © 2011 American Institute of Physics

Numerical Simulation of Blood Flow in Human Artery Using (A, Q) and (A, u) Systems

NASA Astrophysics Data System (ADS)

Mungkasi, Sudi; Wijayanti Budiawan, Inge

2018-03-01

In this paper, we model blood flow in human artery in the form of (𝐴, 𝑄) and (𝐴, 𝑢) systems, then we use the Lax-Friedrichs finite volume method to find the numerical solution of each model. Here 𝐴 represents the cross sectional area of the artery, 𝑄 denotes the discharge of the blood flow, and 𝑢 is the velocity of the blood flow. We simulate the numerical scheme of each model and investigate how the blood pressure pulse propagates in human artery. Particularly, we use the residual of 𝐴 to determine which system is better numerically. We obtain that the (𝐴, 𝑄) system is better numerically than the (𝐴, 𝑢) system, because the absolute of the residual of 𝐴 using the (𝐴, 𝑄) system is smaller than the absolute of the residual of 𝐴 using the (𝐴, 𝑢) system.

Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains

NASA Astrophysics Data System (ADS)

Belyaev, V. A.; Shapeev, V. P.

2017-10-01

New versions of the collocations and least squares method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for the biharmonic equation in non-canonical domains. The solution of the biharmonic equation is used for simulating the stress-strain state of an isotropic plate under the action of transverse load. The differential problem is projected into a space of fourth-degree polynomials by the CLS method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLS method are implemented on the grids which are constructed in two different ways. It is shown that the approximate solution of problems converges with high order. Thus it matches with high accuracy with the analytical solution of the test problems in the case of known solution in the numerical experiments on the convergence of the solution of various problems on a sequence of grids.

An Enriched Shell Element for Delamination Simulation in Composite Laminates

NASA Technical Reports Server (NTRS)

McElroy, Mark

2015-01-01

A formulation is presented for an enriched shell finite element capable of delamination simulation in composite laminates. The element uses an adaptive splitting approach for damage characterization that allows for straightforward low-fidelity model creation and a numerically efficient solution. The Floating Node Method is used in conjunction with the Virtual Crack Closure Technique to predict delamination growth and represent it discretely at an arbitrary ply interface. The enriched element is verified for Mode I delamination simulation using numerical benchmark data. After determining important mesh configuration guidelines for the vicinity of the delamination front in the model, a good correlation was found between the enriched shell element model results and the benchmark data set.

Modelling chemical reactions in dc plasma inside oxygen bubbles in water

NASA Astrophysics Data System (ADS)

Takeuchi, N.; Ishii, Y.; Yasuoka, K.

2012-02-01

Plasmas generated inside oxygen bubbles in water have been developed for water purification. Zero-dimensional numerical simulations were used to investigate the chemical reactions in plasmas driven by dc voltage. The numerical and experimental results of the concentrations of hydrogen peroxide and ozone in the solution were compared with a discharge current between 1 and 7 mA. Upon increasing the water vapour concentration inside bubbles, we saw from the numerical results that the concentration of hydrogen peroxide increased with discharge current, whereas the concentration of ozone decreased. This finding agreed with the experimental results. With an increase in the discharge current, the heat flux from the plasma to the solution increased, and a large amount of water was probably vaporized into the bubbles.

Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Numerical simulation of weakly ionized hypersonic flow over reentry capsules

NASA Astrophysics Data System (ADS)

Scalabrin, Leonardo C.

The mathematical and numerical formulation employed in the development of a new multi-dimensional Computational Fluid Dynamics (CFD) code for the simulation of weakly ionized hypersonic flows in thermo-chemical non-equilibrium over reentry configurations is presented. The flow is modeled using the Navier-Stokes equations modified to include finite-rate chemistry and relaxation rates to compute the energy transfer between different energy modes. The set of equations is solved numerically by discretizing the flowfield using unstructured grids made of any mixture of quadrilaterals and triangles in two-dimensions or hexahedra, tetrahedra, prisms and pyramids in three-dimensions. The partial differential equations are integrated on such grids using the finite volume approach. The fluxes across grid faces are calculated using a modified form of the Steger-Warming Flux Vector Splitting scheme that has low numerical dissipation inside boundary layers. The higher order extension of inviscid fluxes in structured grids is generalized in this work to be used in unstructured grids. Steady state solutions are obtained by integrating the solution over time implicitly. The resulting sparse linear system is solved by using a point implicit or by a line implicit method in which a tridiagonal matrix is assembled by using lines of cells that are formed starting at the wall. An algorithm that assembles these lines using completely general unstructured grids is developed. The code is parallelized to allow simulation of computationally demanding problems. The numerical code is successfully employed in the simulation of several hypersonic entry flows over space capsules as part of its validation process. Important quantities for the aerothermodynamics design of capsules such as aerodynamic coefficients and heat transfer rates are compared to available experimental and flight test data and other numerical results yielding very good agreement. A sensitivity analysis of predicted radiative heating of a space capsule to several thermo-chemical non-equilibrium models is also performed.

Mass-conservative reconstruction of Galerkin velocity fields for transport simulations

NASA Astrophysics Data System (ADS)

Scudeler, C.; Putti, M.; Paniconi, C.

2016-08-01

Accurate calculation of mass-conservative velocity fields from numerical solutions of Richards' equation is central to reliable surface-subsurface flow and transport modeling, for example in long-term tracer simulations to determine catchment residence time distributions. In this study we assess the performance of a local Larson-Niklasson (LN) post-processing procedure for reconstructing mass-conservative velocities from a linear (P1) Galerkin finite element solution of Richards' equation. This approach, originally proposed for a-posteriori error estimation, modifies the standard finite element velocities by imposing local conservation on element patches. The resulting reconstructed flow field is characterized by continuous fluxes on element edges that can be efficiently used to drive a second order finite volume advective transport model. Through a series of tests of increasing complexity that compare results from the LN scheme to those using velocity fields derived directly from the P1 Galerkin solution, we show that a locally mass-conservative velocity field is necessary to obtain accurate transport results. We also show that the accuracy of the LN reconstruction procedure is comparable to that of the inherently conservative mixed finite element approach, taken as a reference solution, but that the LN scheme has much lower computational costs. The numerical tests examine steady and unsteady, saturated and variably saturated, and homogeneous and heterogeneous cases along with initial and boundary conditions that include dry soil infiltration, alternating solute and water injection, and seepage face outflow. Typical problems that arise with velocities derived from P1 Galerkin solutions include outgoing solute flux from no-flow boundaries, solute entrapment in zones of low hydraulic conductivity, and occurrences of anomalous sources and sinks. In addition to inducing significant mass balance errors, such manifestations often lead to oscillations in concentration values that can moreover cause the numerical solution to explode. These problems do not occur when using LN post-processed velocities.

VS2DI: Model use, calibration, and validation

USGS Publications Warehouse

Healy, Richard W.; Essaid, Hedeff I.

2012-01-01

VS2DI is a software package for simulating water, solute, and heat transport through soils or other porous media under conditions of variable saturation. The package contains a graphical preprocessor for constructing simulations, a postprocessor for displaying simulation results, and numerical models that solve for flow and solute transport (VS2DT) and flow and heat transport (VS2DH). Flow is described by the Richards equation, and solute and heat transport are described by advection-dispersion equations; the finite-difference method is used to solve these equations. Problems can be simulated in one, two, or three (assuming radial symmetry) dimensions. This article provides an overview of calibration techniques that have been used with VS2DI; included is a detailed description of calibration procedures used in simulating the interaction between groundwater and a stream fed by drainage from agricultural fields in central Indiana. Brief descriptions of VS2DI and the various types of problems that have been addressed with the software package are also presented.

PFLOTRAN Verification: Development of a Testing Suite to Ensure Software Quality

NASA Astrophysics Data System (ADS)

Hammond, G. E.; Frederick, J. M.

2016-12-01

In scientific computing, code verification ensures the reliability and numerical accuracy of a model simulation by comparing the simulation results to experimental data or known analytical solutions. The model is typically defined by a set of partial differential equations with initial and boundary conditions, and verification ensures whether the mathematical model is solved correctly by the software. Code verification is especially important if the software is used to model high-consequence systems which cannot be physically tested in a fully representative environment [Oberkampf and Trucano (2007)]. Justified confidence in a particular computational tool requires clarity in the exercised physics and transparency in its verification process with proper documentation. We present a quality assurance (QA) testing suite developed by Sandia National Laboratories that performs code verification for PFLOTRAN, an open source, massively-parallel subsurface simulator. PFLOTRAN solves systems of generally nonlinear partial differential equations describing multiphase, multicomponent and multiscale reactive flow and transport processes in porous media. PFLOTRAN's QA test suite compares the numerical solutions of benchmark problems in heat and mass transport against known, closed-form, analytical solutions, including documentation of the exercised physical process models implemented in each PFLOTRAN benchmark simulation. The QA test suite development strives to follow the recommendations given by Oberkampf and Trucano (2007), which describes four essential elements in high-quality verification benchmark construction: (1) conceptual description, (2) mathematical description, (3) accuracy assessment, and (4) additional documentation and user information. Several QA tests within the suite will be presented, including details of the benchmark problems and their closed-form analytical solutions, implementation of benchmark problems in PFLOTRAN simulations, and the criteria used to assess PFLOTRAN's performance in the code verification procedure. References Oberkampf, W. L., and T. G. Trucano (2007), Verification and Validation Benchmarks, SAND2007-0853, 67 pgs., Sandia National Laboratories, Albuquerque, NM.

Numerical simulation of multi-rifled tube drawing - finding proper feedstock dimensions and tool geometry

NASA Astrophysics Data System (ADS)

Bella, P.; Buček, P.; Ridzoň, M.; Mojžiš, M.; Parilák, L.'

2017-02-01

Production of multi-rifled seamless steel tubes is quite a new technology in Železiarne Podbrezová. Therefore, a lot of technological questions emerges (process technology, input feedstock dimensions, material flow during drawing, etc.) Pilot experiments to fine tune the process cost a lot of time and energy. For this, numerical simulation would be an alternative solution for achieving optimal parameters in production technology. This would reduce the number of experiments needed, lowering the overall costs of development. However, to claim the numerical results to be relevant it is necessary to verify them against the actual plant trials. Searching for optimal input feedstock dimension for drawing of multi-rifled tube with dimensions Ø28.6 mm × 6.3 mm is what makes the main topic of this paper. As a secondary task, effective position of the plug - die couple has been solved via numerical simulation. Comparing the calculated results with actual numbers from plant trials a good agreement was observed.

Application of multi-grid method on the simulation of incremental forging processes

NASA Astrophysics Data System (ADS)

Ramadan, Mohamad; Khaled, Mahmoud; Fourment, Lionel

2016-10-01

Numerical simulation becomes essential in manufacturing large part by incremental forging processes. It is a splendid tool allowing to show physical phenomena however behind the scenes, an expensive bill should be paid, that is the computational time. That is why many techniques are developed to decrease the computational time of numerical simulation. Multi-Grid method is a numerical procedure that permits to reduce computational time of numerical calculation by performing the resolution of the system of equations on several mesh of decreasing size which allows to smooth faster the low frequency of the solution as well as its high frequency. In this paper a Multi-Grid method is applied to cogging process in the software Forge 3. The study is carried out using increasing number of degrees of freedom. The results shows that calculation time is divide by two for a mesh of 39,000 nodes. The method is promising especially if coupled with Multi-Mesh method.

Data mining techniques for scientific computing: Application to asymptotic paraxial approximations to model ultrarelativistic particles

NASA Astrophysics Data System (ADS)

Assous, Franck; Chaskalovic, Joël

2011-06-01

We propose a new approach that consists in using data mining techniques for scientific computing. Indeed, data mining has proved to be efficient in other contexts which deal with huge data like in biology, medicine, marketing, advertising and communications. Our aim, here, is to deal with the important problem of the exploitation of the results produced by any numerical method. Indeed, more and more data are created today by numerical simulations. Thus, it seems necessary to look at efficient tools to analyze them. In this work, we focus our presentation to a test case dedicated to an asymptotic paraxial approximation to model ultrarelativistic particles. Our method directly deals with numerical results of simulations and try to understand what each order of the asymptotic expansion brings to the simulation results over what could be obtained by other lower-order or less accurate means. This new heuristic approach offers new potential applications to treat numerical solutions to mathematical models.

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution ofmore » dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.« less

Numerical simulation of time delay Interferometry for LISA with one arm dysfunctional

NASA Astrophysics Data System (ADS)

Ni, Wei-Tou; Dhurandhar, Sanjeev V.; Nayak, K. Rajesh; Wang, Gang

In order to attain the requisite sensitivity for LISA, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. In a previous paper(a), we have found an infinite family of second generation analytic solutions of time delay interferometry and estimated the laser noise due to residual time delay semi-analytically from orbit perturbations due to earth. Since other planets and solar-system bodies also perturb the orbits of LISA spacecraft and affect the time delay interferometry, we simulate the time delay numerically in this paper. To conform to the actual LISA planning, we have worked out a set of 10-year optimized mission orbits of LISA spacecraft using CGC3 ephemeris framework(b). Here we use this numerical solution to calculate the residual errors in the second generation solutions upto n 3 of our previous paper, and compare with the semi-analytic error estimate. The accuracy of this calculation is better than 1 m (or 30 ns). (a) S. V. Dhurandhar, K. Rajesh Nayak and J.-Y. Vinet, time delay Interferometry for LISA with one arm dysfunctional (b) W.-T. Ni and G. Wang, Orbit optimization for 10-year LISA mission orbit starting at 21 June, 2021 using CGC3 ephemeris framework

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 4: Advanced fan section aerodynamic analysis computer program user's manual

NASA Technical Reports Server (NTRS)

Crook, Andrew J.; Delaney, Robert A.

1992-01-01

The computer program user's manual for the ADPACAPES (Advanced Ducted Propfan Analysis Code-Average Passage Engine Simulation) program is included. The objective of the computer program is development of a three-dimensional Euler/Navier-Stokes flow analysis for fan section/engine geometries containing multiple blade rows and multiple spanwise flow splitters. An existing procedure developed by Dr. J. J. Adamczyk and associates at the NASA Lewis Research Center was modified to accept multiple spanwise splitter geometries and simulate engine core conditions. The numerical solution is based upon a finite volume technique with a four stage Runge-Kutta time marching procedure. Multiple blade row solutions are based upon the average-passage system of equations. The numerical solutions are performed on an H-type grid system, with meshes meeting the requirement of maintaining a common axisymmetric mesh for each blade row grid. The analysis was run on several geometry configurations ranging from one to five blade rows and from one to four radial flow splitters. The efficiency of the solution procedure was shown to be the same as the original analysis.

An Extended Trajectory Mechanics Approach for Calculating the Path of a Pressure Transient: Derivation and Illustration

NASA Astrophysics Data System (ADS)

Vasco, D. W.

2018-04-01

Following an approach used in quantum dynamics, an exponential representation of the hydraulic head transforms the diffusion equation governing pressure propagation into an equivalent set of ordinary differential equations. Using a reservoir simulator to determine one set of dependent variables leaves a reduced set of equations for the path of a pressure transient. Unlike the current approach for computing the path of a transient, based on a high-frequency asymptotic solution, the trajectories resulting from this new formulation are valid for arbitrary spatial variations in aquifer properties. For a medium containing interfaces and layers with sharp boundaries, the trajectory mechanics approach produces paths that are compatible with travel time fields produced by a numerical simulator, while the asymptotic solution produces paths that bend too strongly into high permeability regions. The breakdown of the conventional asymptotic solution, due to the presence of sharp boundaries, has implications for model parameter sensitivity calculations and the solution of the inverse problem. For example, near an abrupt boundary, trajectories based on the asymptotic approach deviate significantly from regions of high sensitivity observed in numerical computations. In contrast, paths based on the new trajectory mechanics approach coincide with regions of maximum sensitivity to permeability changes.

Modeling and simulation of different and representative engineering problems using Network Simulation Method

PubMed Central

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model. PMID:29518121

A new potential for the numerical simulations of electrolyte solutions on a hypersphere

NASA Astrophysics Data System (ADS)

Caillol, Jean-Michel

1993-12-01

We propose a new way of performing numerical simulations of the restricted primitive model of electrolytes—and related models—on a hypersphere. In this new approach, the system is viewed as a single component fluid of charged bihard spheres constrained to move at the surface of a four dimensional sphere. A charged bihard sphere is defined as the rigid association of two antipodal charged hard spheres of opposite signs. These objects interact via a simple analytical potential obtained by solving the Poisson-Laplace equation on the hypersphere. This new technique of simulation enables a precise determination of the chemical potential of the charged species in the canonical ensemble by a straightforward application of Widom's insertion method. Comparisons with previous simulations demonstrate the efficiency and the reliability of the method.

Modeling and simulation of different and representative engineering problems using Network Simulation Method.

PubMed

Sánchez-Pérez, J F; Marín, F; Morales, J L; Cánovas, M; Alhama, F

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model.

Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Ju, E-mail: jliu@ices.utexas.edu; Gomez, Hector; Evans, John A.

2013-09-01

We propose a new methodology for the numerical solution of the isothermal Navier–Stokes–Korteweg equations. Our methodology is based on a semi-discrete Galerkin method invoking functional entropy variables, a generalization of classical entropy variables, and a new time integration scheme. We show that the resulting fully discrete scheme is unconditionally stable-in-energy, second-order time-accurate, and mass-conservative. We utilize isogeometric analysis for spatial discretization and verify the aforementioned properties by adopting the method of manufactured solutions and comparing coarse mesh solutions with overkill solutions. Various problems are simulated to show the capability of the method. Our methodology provides a means of constructing unconditionallymore » stable numerical schemes for nonlinear non-convex hyperbolic systems of conservation laws.« less

Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an Eulerian-Lagrangian marker particle technique

NASA Technical Reports Server (NTRS)

Pavish, D. L.; Spaulding, M. L.

1977-01-01

A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.

Revisiting analytical solutions for steady interface flow in subsea aquifers: Aquitard salinity effects

NASA Astrophysics Data System (ADS)

Werner, Adrian D.; Robinson, Neville I.

2018-06-01

Existing analytical solutions for the distribution of fresh groundwater in subsea aquifers presume that the overlying offshore aquitard, represented implicitly, contains seawater. Here, we consider the case where offshore fresh groundwater is the result of freshwater discharge from onshore aquifers, and neglect paleo-freshwater sources. A recent numerical modeling investigation, involving explicit simulation of the offshore aquitard, demonstrates that offshore aquitards more likely contain freshwater in areas of upward freshwater leakage to the sea. We integrate this finding into the existing analytical solutions by providing an alternative formulation for steady interface flow in subsea aquifers, whereby the salinity in the offshore aquitard can be chosen. The new solution, taking the aquitard salinity as that of freshwater, provides a closer match to numerical modeling results in which the aquitard is represented explicitly.

Numerical Simulation of the Oscillations in a Mixer: An Internal Aeroacoustic Feedback System

NASA Technical Reports Server (NTRS)

Jorgenson, Philip C. E.; Loh, Ching Y.

2004-01-01

The space-time conservation element and solution element method is employed to numerically study the acoustic feedback system in a high temperature, high speed wind tunnel mixer. The computation captures the self-sustained feedback loop between reflecting Mach waves and the shear layer. This feedback loop results in violent instabilities that are suspected of causing damage to some tunnel components. The computed frequency is in good agreement with the available experimental data. The physical phenomena are explained based on the numerical results.

A new class of finite element variational multiscale turbulence models for incompressible magnetohydrodynamics

DOE PAGES

Sondak, D.; Shadid, J. N.; Oberai, A. A.; ...

2015-04-29

New large eddy simulation (LES) turbulence models for incompressible magnetohydrodynamics (MHD) derived from the variational multiscale (VMS) formulation for finite element simulations are introduced. The new models include the variational multiscale formulation, a residual-based eddy viscosity model, and a mixed model that combines both of these component models. Each model contains terms that are proportional to the residual of the incompressible MHD equations and is therefore numerically consistent. Moreover, each model is also dynamic, in that its effect vanishes when this residual is small. The new models are tested on the decaying MHD Taylor Green vortex at low and highmore » Reynolds numbers. The evaluation of the models is based on comparisons with available data from direct numerical simulations (DNS) of the time evolution of energies as well as energy spectra at various discrete times. Thus a numerical study, on a sequence of meshes, is presented that demonstrates that the large eddy simulation approaches the DNS solution for these quantities with spatial mesh refinement.« less

Simulation study of the thermal and the thermoelastic effects induced by pulsed laser absorption in human skin

NASA Astrophysics Data System (ADS)

Kim, Jae-Young; Jang, Kyungmin; Yang, Seung-Jin; Baek, Jun-Hyeok; Park, Jong-Rak; Yeom, Dong-Il; Kim, Ji-Sun; Kim, Hyung-Sik; Jun, Jae-Hoon; Chung, Soon-Cheol

2016-04-01

We studied the thermal and the mechanical effects induced by pulsed laser absorption in human skin by numerically solving the heat-transfer and the thermoelastic wave equations. The simulation of the heat-transfer equation yielded the spatiotemporal distribution of the temperature increase in the skin, which was then used in the driving term of the thermoelastic wave equation. We compared our simulation results for the temperature increase and the skin displacements with the measured and numerical results, respectively. For the comparison, we used a recent report by Jun et al. [Sci. Rep. 5, 11016 (2015)], who measured in vivo skin temperature and performed numerical simulation of the thermoelastic wave equation using a simple assumption about the temporal evolution of the temperature distribution, and found their results to be in good agreement with our results. In addition, we obtained solutions for the stresses in the human skin and analyzed their dynamic behaviors in detail.

Nonequilibrium hypersonic flows simulations with asymptotic-preserving Monte Carlo methods

NASA Astrophysics Data System (ADS)

Ren, Wei; Liu, Hong; Jin, Shi

2014-12-01

In the rarefied gas dynamics, the DSMC method is one of the most popular numerical tools. It performs satisfactorily in simulating hypersonic flows surrounding re-entry vehicles and micro-/nano- flows. However, the computational cost is expensive, especially when Kn → 0. Even for flows in the near-continuum regime, pure DSMC simulations require a number of computational efforts for most cases. Albeit several DSMC/NS hybrid methods are proposed to deal with this, those methods still suffer from the boundary treatment, which may cause nonphysical solutions. Filbet and Jin [1] proposed a framework of new numerical methods of Boltzmann equation, called asymptotic preserving schemes, whose computational costs are affordable as Kn → 0. Recently, Ren et al. [2] realized the AP schemes with Monte Carlo methods (AP-DSMC), which have better performance than counterpart methods. In this paper, AP-DSMC is applied in simulating nonequilibrium hypersonic flows. Several numerical results are computed and analyzed to study the efficiency and capability of capturing complicated flow characteristics.

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

NASA Astrophysics Data System (ADS)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

Accurate modelling of unsteady flows in collapsible tubes.

PubMed

Marchandise, Emilie; Flaud, Patrice

2010-01-01

The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1997-07-05

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution.

seismo-live: Training in Computational Seismology using Jupyter Notebooks

NASA Astrophysics Data System (ADS)

Igel, H.; Krischer, L.; van Driel, M.; Tape, C.

2016-12-01

Practical training in computational methodologies is still underrepresented in Earth science curriculae despite the increasing use of sometimes highly sophisticated simulation technologies in research projects. At the same time well-engineered community codes make it easy to return simulation-based results yet with the danger that the inherent traps of numerical solutions are not well understood. It is our belief that training with highly simplified numerical solutions (here to the equations describing elastic wave propagation) with carefully chosen elementary ingredients of simulation technologies (e.g., finite-differencing, function interpolation, spectral derivatives, numerical integration) could substantially improve this situation. For this purpose we have initiated a community platform (www.seismo-live.org) where Python-based Jupyter notebooks can be accessed and run without and necessary downloads or local software installations. The increasingly popular Jupyter notebooks allow combining markup language, graphics, equations with interactive, executable python codes. We demonstrate the potential with training notebooks for the finite-difference method, pseudospectral methods, finite/spectral element methods, the finite-volume and the discontinuous Galerkin method. The platform already includes general Python training, introduction to the ObsPy library for seismology as well as seismic data processing and noise analysis. Submission of Jupyter notebooks for general seismology are encouraged. The platform can be used for complementary teaching in Earth Science courses on compute-intensive research areas.

Numerical Analysis of Dusty-Gas Flows

NASA Astrophysics Data System (ADS)

Saito, T.

2002-02-01

This paper presents the development of a numerical code for simulating unsteady dusty-gas flows including shock and rarefaction waves. The numerical results obtained for a shock tube problem are used for validating the accuracy and performance of the code. The code is then extended for simulating two-dimensional problems. Since the interactions between the gas and particle phases are calculated with the operator splitting technique, we can choose numerical schemes independently for the different phases. A semi-analytical method is developed for the dust phase, while the TVD scheme of Harten and Yee is chosen for the gas phase. Throughout this study, computations are carried out on SGI Origin2000, a parallel computer with multiple of RISC based processors. The efficient use of the parallel computer system is an important issue and the code implementation on Origin2000 is also described. Flow profiles of both the gas and solid particles behind the steady shock wave are calculated by integrating the steady conservation equations. The good agreement between the pseudo-stationary solutions and those from the current numerical code validates the numerical approach and the actual coding. The pseudo-stationary shock profiles can also be used as initial conditions of unsteady multidimensional simulations.

Dynamics of climate-based malaria transmission model with age-structured human population

NASA Astrophysics Data System (ADS)

Addawe, Joel; Pajimola, Aprimelle Kris

2016-10-01

In this paper, we proposed to study the dynamics of malaria transmission with periodic birth rate of the vector and an age-structure for the human population. The human population is divided into two compartments: pre-school (0-5 years) and the rest of the human population. We showed the existence of a disease-free equilibrium point. Using published epidemiological parameters, we use numerical simulations to show potential effect of climate change in the dynamics of age-structured malaria transmission. Numerical simulations suggest that there exists an asymptotically attractive solution that is positive and periodic.

Numerical simulation of swept-wing flows

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1991-01-01

Efforts of the last six months to computationally model the transition process characteristics of flow over swept wings are described. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full 3D Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiment. The leading edge region of a swept wing is considered in a 3D spatial simulation with random disturbances as the initial conditions.

The Effect of Simulated Microgravity Environment of RWV Bioreactors on Surface Reactions and Adsorption of Serum Proteins on Bone-bioactive Microcarriers

NASA Technical Reports Server (NTRS)

Radin, Shula; Ducheyne, P.; Ayyaswamy, P. S.

2003-01-01

Biomimetically modified bioactive materials with bone-like surface properties are attractive candidates for use as microcarriers for 3-D bone-like tissue engineering under simulated microgravity conditions of NASA designed rotating wall vessel (RWV) bioreactors. The simulated microgravity environment is attainable under suitable parametric conditions of the RWV bioreactors. Ca-P containing bioactive glass (BG), whose stimulatory effect on bone cell function had been previously demonstrated, was used in the present study. BG surface modification via reactions in solution, resulting formation of bone-like minerals at the surface and adsorption of serum proteins is critical for obtaining the stimulatory effect. In this paper, we report on the major effects of simulated microgravity conditions of the RWV on the BG reactions surface reactions and protein adsorption in physiological solutions. Control tests at normal gravity were conducted at static and dynamic conditions. The study revealed that simulated microgravity remarkably enhanced reactions involved in the BG surface modification, including BG dissolution, formation of bone-like minerals at the surface and adsorption of serum proteins. Simultaneously, numerical models were developed to simulate the mass transport of chemical species to and from the BG surface under normal gravity and simulated microgravity conditions. The numerical results showed an excellent agreement with the experimental data at both testing conditions.

Simulation Applications at NASA Ames Research Center

NASA Technical Reports Server (NTRS)

Inouye, M.

1984-01-01

Aeronautical applications of simulation technology at Ames Research Center are described. The largest wind tunnel in the world is used to determine the flow field and aerodynamic characteristics of various aircraft, helicopter, and missile configurations. Large computers are used to obtain similar results through numerical solutions of the governing equations. Capabilities are illustrated by computer simulations of turbulence, aileron buzz, and an exhaust jet. Flight simulators are used to assess the handling qualities of advanced aircraft, particularly during takeoff and landing.

Numerical and experimental investigation of light trapping effect of nanostructured diatom frustules

NASA Astrophysics Data System (ADS)

Chen, Xiangfan; Wang, Chen; Baker, Evan; Sun, Cheng

2015-07-01

Recent advances in nanophotonic light-trapping technologies offer promising solutions in developing high-efficiency thin-film solar cells. However, the cost-effective scalable manufacturing of those rationally designed nanophotonic structures remains a critical challenge. In contrast, diatoms, the most common type of phytoplankton found in nature, may offer a very attractive solution. Diatoms exhibit high solar energy harvesting efficiency due to their frustules (i.e., hard porous cell wall made of silica) possessing remarkable hierarchical micro-/nano-scaled features optimized for the photosynthetic process through millions of years of evolution. Here we report numerical and experimental studies to investigate the light-trapping characteristic of diatom frustule. Rigorous coupled wave analysis (RCWA) and finite-difference time-domain (FDTD) methods are employed to investigate the light-trapping characteristics of the diatom frustules. In simulation, placing the diatom frustules on the surface of the light-absorption materials is found to strongly enhance the optical absorption over the visible spectrum. The absorption spectra are also measured experimentally and the results are in good agreement with numerical simulations.

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation

PubMed Central

Botello-Smith, Wesley M.; Luo, Ray

2016-01-01

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966

Large calculation of the flow over a hypersonic vehicle using a GPU

NASA Astrophysics Data System (ADS)

Elsen, Erich; LeGresley, Patrick; Darve, Eric

2008-12-01

Graphics processing units are capable of impressive computing performance up to 518 Gflops peak performance. Various groups have been using these processors for general purpose computing; most efforts have focussed on demonstrating relatively basic calculations, e.g. numerical linear algebra, or physical simulations for visualization purposes with limited accuracy. This paper describes the simulation of a hypersonic vehicle configuration with detailed geometry and accurate boundary conditions using the compressible Euler equations. To the authors' knowledge, this is the most sophisticated calculation of this kind in terms of complexity of the geometry, the physical model, the numerical methods employed, and the accuracy of the solution. The Navier-Stokes Stanford University Solver (NSSUS) was used for this purpose. NSSUS is a multi-block structured code with a provably stable and accurate numerical discretization which uses a vertex-based finite-difference method. A multi-grid scheme is used to accelerate the solution of the system. Based on a comparison of the Intel Core 2 Duo and NVIDIA 8800GTX, speed-ups of over 40× were demonstrated for simple test geometries and 20× for complex geometries.

Using exact solutions to develop an implicit scheme for the baroclinic primitive equations

NASA Technical Reports Server (NTRS)

Marchesin, D.

1984-01-01

The exact solutions presently obtained by means of a novel method for nonlinear initial value problems are used in the development of numerical schemes for the computer solution of these problems. The method is applied to a new, fully implicit scheme on a vertical slice of the isentropic baroclinic equations. It was not possible to find a global scale phenomenon that could be simulated by the baroclinic primitive equations on a vertical slice.

Approximate analytic expression for the Skyrmions crystal

NASA Astrophysics Data System (ADS)

Grandi, Nicolás; Sturla, Mauricio

2018-01-01

We find approximate solutions for the two-dimensional nonlinear Σ-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

Structure of field rotating disturbances in warm plasma

NASA Technical Reports Server (NTRS)

Wolfson, R.

1982-01-01

A model in which thermal effects are simulated through use of a multibeam plasma distribution function is developed and investigated to see if solutions which take an initially uniform magnetized plasma to a new uniform state with different field orientation are possible. The momentum conservation integrals are found to admit two classes of such solutions, but only one class exhibits appropriate asymptotic behavior. Extensive numerical integrations have failed to demonstrate the existence of the desired solutions.

Convergence studies in meshfree peridynamic simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seleson, Pablo; Littlewood, David J.

2016-04-15

Meshfree methods are commonly applied to discretize peridynamic models, particularly in numerical simulations of engineering problems. Such methods discretize peridynamic bodies using a set of nodes with characteristic volume, leading to particle-based descriptions of systems. In this article, we perform convergence studies of static peridynamic problems. We show that commonly used meshfree methods in peridynamics suffer from accuracy and convergence issues, due to a rough approximation of the contribution to the internal force density of nodes near the boundary of the neighborhood of a given node. We propose two methods to improve meshfree peridynamic simulations. The first method uses accuratemore » computations of volumes of intersections between neighbor cells and the neighborhood of a given node, referred to as partial volumes. The second method employs smooth influence functions with a finite support within peridynamic kernels. Numerical results demonstrate great improvements in accuracy and convergence of peridynamic numerical solutions, when using the proposed methods.« less

Direct Numerical Simulation of Passive Scalar Mixing in Shock Turbulence Interaction

NASA Astrophysics Data System (ADS)

Gao, Xiangyu; Bermejo-Moreno, Ivan; Larsson, Johan

2017-11-01

Passive scalar mixing in the canonical shock-turbulence interaction configuration is investigated through shock-capturing Direct Numerical Simulations (DNS). Scalar fields with different Schmidt numbers are transported by an initially isotropic turbulent flow field passing across a nominally planar shock wave. A solution-adaptive hybrid numerical scheme on Cartesian structured grids is used, that combines a fifth-order WENO scheme near shocks and a sixth-order central-difference scheme away from shocks. The simulations target variations in the shock Mach number, M (from 1.5 to 3), turbulent Mach number, Mt (from 0.1 to 0.4, including wrinkled- and broken-shock regimes), and scalar Schmidt numbers, Sc (from 0.5 to 2), while keeping the Taylor microscale Reynolds number constant (Reλ 40). The effects on passive scalar statistics are investigated, including the streamwise evolution of scalar variance budgets, pdfs and spectra, in comparison with their temporal evolution in decaying isotropic turbulence.

Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow

NASA Astrophysics Data System (ADS)

Tsvelodub, O. Yu; Bocharov, A. A.

2017-09-01

The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. The paper studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. The periodic and soliton steady-state traveling solutions of this equation have been numerically found. The analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that this model equation has solutions in the form of solitons-humps.

Numerical Simulation of Rheological, Chemical and Hydromechanical Processes of Thrombolysis

NASA Astrophysics Data System (ADS)

Khramchenkov, E.; Khramchenkov, M.

2015-04-01

Mathematical model of clot lysis in blood vessels is developed on the basis of equations of convection-diffusion. Fibrin of the clot is considered stationary solid phase, and plasminogen, plasmin and plasminogen-activators - as dissolved fluid phases. As a result of numerical solution of the model predictions of lysis process are gained. Important influence of clot swelling on the process of lysis is revealed.

A Numerical Study on Microwave Coagulation Therapy

DTIC Science & Technology

2013-01-01

hepatocellular carcinoma (small size liver tumor). Through extensive numerical simulations, we reveal the mathematical relationships between some critical parameters in the therapy, including input power, frequency, temperature, and regions of impact. It is shown that these relationships can be approximated using simple polynomial functions. Compared to solutions of partial differential equations, these functions are significantly easier to compute and simpler to analyze for engineering design and clinical

An MPI-based MoSST core dynamics model

NASA Astrophysics Data System (ADS)

Jiang, Weiyuan; Kuang, Weijia

2008-09-01

Distributed systems are among the main cost-effective and expandable platforms for high-end scientific computing. Therefore scalable numerical models are important for effective use of such systems. In this paper, we present an MPI-based numerical core dynamics model for simulation of geodynamo and planetary dynamos, and for simulation of core-mantle interactions. The model is developed based on MPI libraries. Two algorithms are used for node-node communication: a "master-slave" architecture and a "divide-and-conquer" architecture. The former is easy to implement but not scalable in communication. The latter is scalable in both computation and communication. The model scalability is tested on Linux PC clusters with up to 128 nodes. This model is also benchmarked with a published numerical dynamo model solution.

Prediction of sound absorption in rigid porous media with the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

da Silva, Andrey Ricardo; Mareze, Paulo; Brandão, Eric

2016-02-01

In this work, sound absorption phenomena associated with the viscous shear stress within rigid porous media is investigated with a simple isothermal lattice Boltzmann BGK model. Simulations are conducted for different macroscopic material properties such as sample thickness and porosity and the results are compared with the exact analytical solution for materials with slit-like structure in terms of acoustic impedance and sound absorption coefficient. The numerical results agree very well with the exact solution, particularly for the sound absorption coefficient. The small deviations found in the low frequency limit for the real part of the acoustic impedance are attributed to the ratio between the thicknesses of the slit and the viscous boundary layer. The results suggest that the lattice Boltzmann method can be a very compelling numerical tool for simulating viscous sound absorption phenomena in the time domain, particularly due to its computational simplicity when compared to traditional continuum based techniques.

A three-dimensional, time-dependent model of Mobile Bay

NASA Technical Reports Server (NTRS)

Pitts, F. H.; Farmer, R. C.

1976-01-01

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Numerical Simulation of Subsonic and Transonic Propeller Flow. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Snyder, Aaron

1988-01-01

The numerical simulation of 3-D transonic flow about a system of propeller blades is investigated. In particular, it is shown that the use of helical coordinates significantly simplifies the form of the governing equation when the propeller system is assumed to be surrounded by an irrotational flow field of an inviscid fluid. The unsteady small disturbance equation, valid for lightly loaded blades and expressed in helical coordinates, is derived from the general blade-fixed potential equation, given for an arbitrary coordinate system. The use of a coordinate system which inherently adapts to the mean flow results in a disturbance equation requiring relatively few terms to accurately model the physics of the flow. Furthermore, the helical coordinate system presented here is novel in that it is periodic in the circumferential direction while, simultaneously, maintaining orthogonal properties at the mean blade locations. The periodic characteristic allows a complete cascade of blades to be treated, and the orthogonality property affords straightforward treatment of blade boundary conditions. An ADI numerical scheme is used to compute the solution of the steady flow as an asymptotic limit of an unsteady flow. As an example of the method, solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an 8-bladed cascade. Both high and low advance ratio cases are computed and include a lifting as well as nonlifting cases. The nonlifting solutions obtained are compared to solutions from a Euler code.

Wavelet-based Adaptive Mesh Refinement Method for Global Atmospheric Chemical Transport Modeling

NASA Astrophysics Data System (ADS)

Rastigejev, Y.

2011-12-01

Numerical modeling of global atmospheric chemical transport presents enormous computational difficulties, associated with simulating a wide range of time and spatial scales. The described difficulties are exacerbated by the fact that hundreds of chemical species and thousands of chemical reactions typically are used for chemical kinetic mechanism description. These computational requirements very often forces researches to use relatively crude quasi-uniform numerical grids with inadequate spatial resolution that introduces significant numerical diffusion into the system. It was shown that this spurious diffusion significantly distorts the pollutant mixing and transport dynamics for typically used grid resolution. The described numerical difficulties have to be systematically addressed considering that the demand for fast, high-resolution chemical transport models will be exacerbated over the next decade by the need to interpret satellite observations of tropospheric ozone and related species. In this study we offer dynamically adaptive multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of atmospheric chemical evolution equations. The adaptive mesh refinement is performed by adding and removing finer levels of resolution in the locations of fine scale development and in the locations of smooth solution behavior accordingly. The algorithm is based on the mathematically well established wavelet theory. This allows us to provide error estimates of the solution that are used in conjunction with an appropriate threshold criteria to adapt the non-uniform grid. Other essential features of the numerical algorithm include: an efficient wavelet spatial discretization that allows to minimize the number of degrees of freedom for a prescribed accuracy, a fast algorithm for computing wavelet amplitudes, and efficient and accurate derivative approximations on an irregular grid. The method has been tested for a variety of benchmark problems including numerical simulation of transpacific traveling pollution plumes. The generated pollution plumes are diluted due to turbulent mixing as they are advected downwind. Despite this dilution, it was recently discovered that pollution plumes in the remote troposphere can preserve their identity as well-defined structures for two weeks or more as they circle the globe. Present Global Chemical Transport Models (CTMs) implemented for quasi-uniform grids are completely incapable of reproducing these layered structures due to high numerical plume dilution caused by numerical diffusion combined with non-uniformity of atmospheric flow. It is shown that WAMR algorithm solutions of comparable accuracy as conventional numerical techniques are obtained with more than an order of magnitude reduction in number of grid points, therefore the adaptive algorithm is capable to produce accurate results at a relatively low computational cost. The numerical simulations demonstrate that WAMR algorithm applied the traveling plume problem accurately reproduces the plume dynamics unlike conventional numerical methods that utilizes quasi-uniform numerical grids.

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

EXTENSION OF THE MURAM RADIATIVE MHD CODE FOR CORONAL SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rempel, M., E-mail: rempel@ucar.edu

2017-01-01

We present a new version of the MURaM radiative magnetohydrodynamics (MHD) code that allows for simulations spanning from the upper convection zone into the solar corona. We implement the relevant coronal physics in terms of optically thin radiative loss, field aligned heat conduction, and an equilibrium ionization equation of state. We artificially limit the coronal Alfvén and heat conduction speeds to computationally manageable values using an approximation to semi-relativistic MHD with an artificially reduced speed of light (Boris correction). We present example solutions ranging from quiet to active Sun in order to verify the validity of our approach. We quantifymore » the role of numerical diffusivity for the effective coronal heating. We find that the (numerical) magnetic Prandtl number determines the ratio of resistive to viscous heating and that owing to the very large magnetic Prandtl number of the solar corona, heating is expected to happen predominantly through viscous dissipation. We find that reasonable solutions can be obtained with values of the reduced speed of light just marginally larger than the maximum sound speed. Overall this leads to a fully explicit code that can compute the time evolution of the solar corona in response to photospheric driving using numerical time steps not much smaller than 0.1 s. Numerical simulations of the coronal response to flux emergence covering a time span of a few days are well within reach using this approach.« less

Fast neural solution of a nonlinear wave equation

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad; Barhen, Jacob

1992-01-01

A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.

Particle Simulations in Magnetospheric Plasmas

DTIC Science & Technology

1989-12-18

Foreshock As an application of the simulation method used in the proposed research (Broadband electrostatic noise), the beam instability in the... foreshock has been investigated. Electrons backstreaming into the Earth’s foreshock generate waves near the plasma frequency by the beam instability. Two...results and numerical solutions of the dispersion equation indicate that the center frequency of the intense narrowband waves near the foreshock boundary

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model.

PubMed

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-28

The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.

Numerical simulation the pollutants transport in the Lake base on remote sensing image with Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Qiao, Y.

2013-12-01

As China's economic development, water pollution incidents happened frequently. For example, the cyanobacterial bloom events repeatedly occur in Taihu Lake. In this research, we investigate the pollutants solute transport start at different points, such as the eutrophication substances Nitrogen and Phosphorus et al, with the Lattice Boltzmann Method (LBM) performed on real pore geometries. The LBM has emerged as a powerful tool for simulating the behaviour of multi-component fluid systems in complex pore networks. We will build a quick response simulation system, which is base on the high resolution GIS figure, using the LBM numerical method.When the start two deferent points at the Meiliang Bay nearby the Wuxi City, it is shown that the pollutants solute can't transport out of the bay to influence the Taihu Lake and the diffusion areas are similar. On the other hand, when the start point at central region of the Taihu Lake, it is found that the pollutants solute covered the almost whole area of the lake and the cyanobacterial bloom with good condition. In the same way, if the cyanobacterial bloom transport in the central area, then it will pollute the whole Taihu Lake. Therefore, when we monitor and deal with the eutrophication substances, we need to focus on the central area of lake.

Development and Implementation of a Transport Method for the Transport and Reaction Simulation Engine (TaRSE) based on the Godunov-Mixed Finite Element Method

USGS Publications Warehouse

James, Andrew I.; Jawitz, James W.; Munoz-Carpena, Rafael

2009-01-01

A model to simulate transport of materials in surface water and ground water has been developed to numerically approximate solutions to the advection-dispersion equation. This model, known as the Transport and Reaction Simulation Engine (TaRSE), uses an algorithm that incorporates a time-splitting technique where the advective part of the equation is solved separately from the dispersive part. An explicit finite-volume Godunov method is used to approximate the advective part, while a mixed-finite element technique is used to approximate the dispersive part. The dispersive part uses an implicit discretization, which allows it to run stably with a larger time step than the explicit advective step. The potential exists to develop algorithms that run several advective steps, and then one dispersive step that encompasses the time interval of the advective steps. Because the dispersive step is computationally most expensive, schemes can be implemented that are more computationally efficient than non-time-split algorithms. This technique enables scientists to solve problems with high grid Peclet numbers, such as transport problems with sharp solute fronts, without spurious oscillations in the numerical approximation to the solution and with virtually no artificial diffusion.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

NASA Technical Reports Server (NTRS)

Mitchell, L. D.; David, J. W.

1983-01-01

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

Alternans and Spiral Breakup in an Excitable Reaction-Diffusion System: A Simulation Study

PubMed Central

Gani, M. Osman; Ogawa, Toshiyuki

2014-01-01

The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context of cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation. The latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of periodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered model. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia). We show that the spiral wave breakup is a consequence of the transverse instability of the planar traveling wave solutions. The alternans, that is, the oscillation of pulse widths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the stable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions. The spiral breakup occurs far below the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes more pronounced. PMID:27379274

Alternans and Spiral Breakup in an Excitable Reaction-Diffusion System: A Simulation Study.

PubMed

Gani, M Osman; Ogawa, Toshiyuki

2014-01-01

The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context of cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation. The latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of periodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered model. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia). We show that the spiral wave breakup is a consequence of the transverse instability of the planar traveling wave solutions. The alternans, that is, the oscillation of pulse widths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the stable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions. The spiral breakup occurs far below the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes more pronounced.

Numerical simulation of pseudoelastic shape memory alloys using the large time increment method

NASA Astrophysics Data System (ADS)

Gu, Xiaojun; Zhang, Weihong; Zaki, Wael; Moumni, Ziad

2017-04-01

The paper presents a numerical implementation of the large time increment (LATIN) method for the simulation of shape memory alloys (SMAs) in the pseudoelastic range. The method was initially proposed as an alternative to the conventional incremental approach for the integration of nonlinear constitutive models. It is adapted here for the simulation of pseudoelastic SMA behavior using the Zaki-Moumni model and is shown to be especially useful in situations where the phase transformation process presents little or lack of hardening. In these situations, a slight stress variation in a load increment can result in large variations of strain and local state variables, which may lead to difficulties in numerical convergence. In contrast to the conventional incremental method, the LATIN method solve the global equilibrium and local consistency conditions sequentially for the entire loading path. The achieved solution must satisfy the conditions of static and kinematic admissibility and consistency simultaneously after several iterations. 3D numerical implementation is accomplished using an implicit algorithm and is then used for finite element simulation using the software Abaqus. Computational tests demonstrate the ability of this approach to simulate SMAs presenting flat phase transformation plateaus and subjected to complex loading cases, such as the quasi-static behavior of a stent structure. Some numerical results are contrasted to those obtained using step-by-step incremental integration.

Assessment of a Hybrid Continuous/Discontinuous Galerkin Finite Element Code for Geothermal Reservoir Simulations

DOE PAGES

Xia, Yidong; Podgorney, Robert; Huang, Hai

2016-03-17

FALCON (“Fracturing And Liquid CONvection”) is a hybrid continuous / discontinuous Galerkin finite element geothermal reservoir simulation code based on the MOOSE (“Multiphysics Object-Oriented Simulation Environment”) framework being developed and used for multiphysics applications. In the present work, a suite of verification and validation (“V&V”) test problems for FALCON was defined to meet the design requirements, and solved to the interests of enhanced geothermal system (“EGS”) design. Furthermore, the intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the FALCON solution methods. The simulation problems vary in complexity from singly mechanical ormore » thermo process, to coupled thermo-hydro-mechanical processes in geological porous media. Numerical results obtained by FALCON agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these capabilities in FALCON. Some form of solution verification has been attempted to identify sensitivities in the solution methods, where possible, and suggest best practices when using the FALCON code.« less

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

DOE PAGES

Xia, Yidong; Wang, Chuanjin; Luo, Hong; ...

2015-12-15

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Yidong; Wang, Chuanjin; Luo, Hong

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less

Application of fractional derivative with exponential law to bi-fractional-order wave equation with frictional memory kernel

NASA Astrophysics Data System (ADS)

Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-12-01

Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.

Cosmic-ray propagation with DRAGON2: I. numerical solver and astrophysical ingredients

NASA Astrophysics Data System (ADS)

Evoli, Carmelo; Gaggero, Daniele; Vittino, Andrea; Di Bernardo, Giuseppe; Di Mauro, Mattia; Ligorini, Arianna; Ullio, Piero; Grasso, Dario

2017-02-01

We present version 2 of the DRAGON code designed for computing realistic predictions of the CR densities in the Galaxy. The code numerically solves the interstellar CR transport equation (including inhomogeneous and anisotropic diffusion, either in space and momentum, advective transport and energy losses), under realistic conditions. The new version includes an updated numerical solver and several models for the astrophysical ingredients involved in the transport equation. Improvements in the accuracy of the numerical solution are proved against analytical solutions and in reference diffusion scenarios. The novel features implemented in the code allow to simulate the diverse scenarios proposed to reproduce the most recent measurements of local and diffuse CR fluxes, going beyond the limitations of the homogeneous galactic transport paradigm. To this end, several applications using DRAGON2 are presented as well. This new version facilitates the users to include their own physical models by means of a modular C++ structure.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

PIC simulations of a three component plasma described by Kappa distribution functions as observed in Saturn's magnetosphere

NASA Astrophysics Data System (ADS)

Barbosa, Marcos; Alves, Maria Virginia; Simões Junior, Fernando

2016-04-01

In plasmas out of thermodynamic equilibrium the particle velocity distribution can be described by the so called Kappa distribution. These velocity distribution functions are a generalization of the Maxwellian distribution. Since 1960, Kappa velocity distributions were observed in several regions of interplanetary space and astrophysical plasmas. Using KEMPO1 particle simulation code, modified to introduce Kappa distribution functions as initial conditions for particle velocities, the normal modes of propagation were analyzed in a plasma containing two species of electrons with different temperatures and densities and ions as a third specie.This type of plasma is usually found in magnetospheres such as in Saturn. Numerical solutions for the dispersion relation for such a plasma predict the presence of an electron-acoustic mode, besides the Langmuir and ion-acoustic modes. In the presence of an ambient magnetic field, the perpendicular propagation (Bernstein mode) also changes, as compared to a Maxwellian plasma, due to the Kappa distribution function. Here results for simulations with and without external magnetic field are presented. The parameters for the initial conditions in the simulations were obtained from the Cassini spacecraft data. Simulation results are compared with numerical solutions of the dispersion relation obtained in the literature and they are in good agreement.

Numerical Simulations of Vortex Generator Vanes and Jets on a Flat Plate

NASA Technical Reports Server (NTRS)

Allan, Brian G.; Yao, Chung-Sheng; Lin, John C.

2002-01-01

Numerical simulations of a single low-profile vortex generator vane, which is only a small fraction of the boundary-layer thickness, and a vortex generating jet have been performed for flows over a flat plate. The numerical simulations were computed by solving the steady-state solution to the Reynolds-averaged Navier-Stokes equations. The vortex generating vane results were evaluated by comparing the strength and trajectory of the streamwise vortex to experimental particle image velocimetry measurements. From the numerical simulations of the vane case, it was observed that the Shear-Stress Transport (SST) turbulence model resulted in a better prediction of the streamwise peak vorticity and trajectory when compared to the Spalart-Allmaras (SA) turbulence model. It is shown in this investigation that the estimation of the turbulent eddy viscosity near the vortex core, for both the vane and jet simulations, was higher for the SA model when compared to the SST model. Even though the numerical simulations of the vortex generating vane were able to predict the trajectory of the stream-wise vortex, the initial magnitude and decay of the peak streamwise vorticity were significantly under predicted. A comparison of the positive circulation associated with the streamwise vortex showed that while the numerical simulations produced a more diffused vortex, the vortex strength compared very well to the experimental observations. A grid resolution study for the vortex generating vane was also performed showing that the diffusion of the vortex was not a result of insufficient grid resolution. Comparisons were also made between a fully modeled trapezoidal vane with finite thickness to a simply modeled rectangular thin vane. The comparisons showed that the simply modeled rectangular vane produced a streamwise vortex which had a strength and trajectory very similar to the fully modeled trapezoidal vane.

Simulations of reactive transport and precipitation with smoothed particle hydrodynamics

NASA Astrophysics Data System (ADS)

Tartakovsky, Alexandre M.; Meakin, Paul; Scheibe, Timothy D.; Eichler West, Rogene M.

2007-03-01

A numerical model based on smoothed particle hydrodynamics (SPH) was developed for reactive transport and mineral precipitation in fractured and porous materials. Because of its Lagrangian particle nature, SPH has several advantages for modeling Navier-Stokes flow and reactive transport including: (1) in a Lagrangian framework there is no non-linear term in the momentum conservation equation, so that accurate solutions can be obtained for momentum dominated flows and; (2) complicated physical and chemical processes such as surface growth due to precipitation/dissolution and chemical reactions are easy to implement. In addition, SPH simulations explicitly conserve mass and linear momentum. The SPH solution of the diffusion equation with fixed and moving reactive solid-fluid boundaries was compared with analytical solutions, Lattice Boltzmann [Q. Kang, D. Zhang, P. Lichtner, I. Tsimpanogiannis, Lattice Boltzmann model for crystal growth from supersaturated solution, Geophysical Research Letters, 31 (2004) L21604] simulations and diffusion limited aggregation (DLA) [P. Meakin, Fractals, scaling and far from equilibrium. Cambridge University Press, Cambridge, UK, 1998] model simulations. To illustrate the capabilities of the model, coupled three-dimensional flow, reactive transport and precipitation in a fracture aperture with a complex geometry were simulated.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Comparison of updated Lagrangian FEM with arbitrary Lagrangian Eulerian method for 3D thermo-mechanical extrusion of a tube profile

NASA Astrophysics Data System (ADS)

Kronsteiner, J.; Horwatitsch, D.; Zeman, K.

2017-10-01

Thermo-mechanical numerical modelling and simulation of extrusion processes faces several serious challenges. Large plastic deformations in combination with a strong coupling of thermal with mechanical effects leads to a high numerical demand for the solution as well as for the handling of mesh distortions. The two numerical methods presented in this paper also reflect two different ways to deal with mesh distortions. Lagrangian Finite Element Methods (FEM) tackle distorted elements by building a new mesh (called re-meshing) whereas Arbitrary Lagrangian Eulerian (ALE) methods use an "advection" step to remap the solution from the distorted to the undistorted mesh. Another difference between conventional Lagrangian and ALE methods is the separate treatment of material and mesh in ALE, allowing the definition of individual velocity fields. In theory, an ALE formulation contains the Eulerian formulation as a subset to the Lagrangian description of the material. The investigations presented in this paper were dealing with the direct extrusion of a tube profile using EN-AW 6082 aluminum alloy and a comparison of experimental with Lagrangian and ALE results. The numerical simulations cover the billet upsetting and last until one third of the billet length is extruded. A good qualitative correlation of experimental and numerical results could be found, however, major differences between Lagrangian and ALE methods concerning thermo-mechanical coupling lead to deviations in the thermal results.

On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo

2017-06-01

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, ofmore » the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.« less

A simulation study of homogeneous ice nucleation in supercooled salty water

NASA Astrophysics Data System (ADS)

Soria, Guiomar D.; Espinosa, Jorge R.; Ramirez, Jorge; Valeriani, Chantal; Vega, Carlos; Sanz, Eduardo

2018-06-01

We use computer simulations to investigate the effect of salt on homogeneous ice nucleation. The melting point of the employed solution model was obtained both by direct coexistence simulations and by thermodynamic integration from previous calculations of the water chemical potential. Using a seeding approach, in which we simulate ice seeds embedded in a supercooled aqueous solution, we compute the nucleation rate as a function of temperature for a 1.85 NaCl mol per water kilogram solution at 1 bar. To improve the accuracy and reliability of our calculations, we combine seeding with the direct computation of the ice-solution interfacial free energy at coexistence using the Mold Integration method. We compare the results with previous simulation work on pure water to understand the effect caused by the solute. The model captures the experimental trend that the nucleation rate at a given supercooling decreases when adding salt. Despite the fact that the thermodynamic driving force for ice nucleation is higher for salty water for a given supercooling, the nucleation rate slows down with salt due to a significant increase of the ice-fluid interfacial free energy. The salty water model predicts an ice nucleation rate that is in good agreement with experimental measurements, bringing confidence in the predictive ability of the model. We expect that the combination of state-of-the-art simulation methods here employed to study ice nucleation from solution will be of much use in forthcoming numerical investigations of crystallization in mixtures.

A simulation study of homogeneous ice nucleation in supercooled salty water.

PubMed

Soria, Guiomar D; Espinosa, Jorge R; Ramirez, Jorge; Valeriani, Chantal; Vega, Carlos; Sanz, Eduardo

2018-06-14

We use computer simulations to investigate the effect of salt on homogeneous ice nucleation. The melting point of the employed solution model was obtained both by direct coexistence simulations and by thermodynamic integration from previous calculations of the water chemical potential. Using a seeding approach, in which we simulate ice seeds embedded in a supercooled aqueous solution, we compute the nucleation rate as a function of temperature for a 1.85 NaCl mol per water kilogram solution at 1 bar. To improve the accuracy and reliability of our calculations, we combine seeding with the direct computation of the ice-solution interfacial free energy at coexistence using the Mold Integration method. We compare the results with previous simulation work on pure water to understand the effect caused by the solute. The model captures the experimental trend that the nucleation rate at a given supercooling decreases when adding salt. Despite the fact that the thermodynamic driving force for ice nucleation is higher for salty water for a given supercooling, the nucleation rate slows down with salt due to a significant increase of the ice-fluid interfacial free energy. The salty water model predicts an ice nucleation rate that is in good agreement with experimental measurements, bringing confidence in the predictive ability of the model. We expect that the combination of state-of-the-art simulation methods here employed to study ice nucleation from solution will be of much use in forthcoming numerical investigations of crystallization in mixtures.

Numerical solutions of atmospheric flow over semielliptical simulated hills

NASA Technical Reports Server (NTRS)

Shieh, C. F.; Frost, W.

1981-01-01

Atmospheric motion over obstacles on plane surfaces to compute simulated wind fields over terrain features was studied. Semielliptical, two dimensional geometry and numerical simulation of flow over rectangular geometries is also discussed. The partial differential equations for the vorticity, stream function, turbulence kinetic energy, and turbulence length scale were solved by a finite difference technique. The mechanism of flow separation induced by a semiellipse is the same as flow over a gradually sloping surface for which the flow separation is caused by the interaction between the viscous force, the pressure force, and the turbulence level. For flow over bluff bodies, a downstream recirculation bubble is created which increases the aspect ratio and/or the turbulence level results in flow reattachment close behind the obstacle.

Direct Numerical Simulation of a Coolant Jet in a Periodic Crossflow

NASA Technical Reports Server (NTRS)

Sharma, Chirdeep; Acharya, Sumanta

1998-01-01

A Direct Numerical Simulation of a coolant jet injected normally into a periodic crossflow is presented. The physical situation simulated represents a periodic module in a coolant hole array with a heated crossflow. A collocated finite difference scheme is used which is fifth-order accurate spatially and second-order accurate temporally. The scheme is based on a fractional step approach and requires the solution of a pressure-Poisson equation. The simulations are obtained for a blowing ratio of 0.25 and a channel Reynolds number of 5600. The simulations reveal the dynamics of several large scale structures including the Counter-rotating Vortex Pair (CVP), the horse-shoe vortex, the shear layer vortex, the wall vortex and the wake vortex. The origins and the interactions of these vortical structures are identified and explored. Also presented are the turbulence statistics and how they relate to the flow structures.

Simulations of 6-DOF Motion with a Cartesian Method

NASA Technical Reports Server (NTRS)

Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan (Technical Monitor)

2003-01-01

Coupled 6-DOF/CFD trajectory predictions using an automated Cartesian method are demonstrated by simulating a GBU-32/JDAM store separating from an F-18C aircraft. Numerical simulations are performed at two Mach numbers near the sonic speed, and compared with flight-test telemetry and photographic-derived data. Simulation results obtained with a sequential-static series of flow solutions are contrasted with results using a time-dependent flow solver. Both numerical methods show good agreement with the flight-test data through the first half of the simulations. The sequential-static and time-dependent methods diverge over the last half of the trajectory prediction. after the store produces peak angular rates. A cost comparison for the Cartesian method is included, in terms of absolute cost and relative to computing uncoupled 6-DOF trajectories. A detailed description of the 6-DOF method, as well as a verification of its accuracy, is provided in an appendix.

Numerical Validation of Chemical Compositional Model for Wettability Alteration Processes

NASA Astrophysics Data System (ADS)

Bekbauov, Bakhbergen; Berdyshev, Abdumauvlen; Baishemirov, Zharasbek; Bau, Domenico

2017-12-01

Chemical compositional simulation of enhanced oil recovery and surfactant enhanced aquifer remediation processes is a complex task that involves solving dozens of equations for all grid blocks representing a reservoir. In the present work, we perform a numerical validation of the newly developed mathematical formulation which satisfies the conservation laws of mass and energy and allows applying a sequential solution approach to solve the governing equations separately and implicitly. Through its application to the numerical experiment using a wettability alteration model and comparisons with existing chemical compositional model's numerical results, the new model has proven to be practical, reliable and stable.

Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state

NASA Astrophysics Data System (ADS)

Lee, Bok Jik; Toro, Eleuterio F.; Castro, Cristóbal E.; Nikiforakis, Nikolaos

2013-08-01

For the numerical simulation of detonation of condensed phase explosives, a complex equation of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Cochran-Chan (C-C) EOS, are widely used. However, when a conservative scheme is used for solving the Euler equations with such equations of state, a spurious solution across the contact discontinuity, a well known phenomenon in multi-fluid systems, arises even for single materials. In this work, we develop a generalised Osher-type scheme in an adaptive primitive-conservative framework to overcome the aforementioned difficulties. Resulting numerical solutions are compared with the exact solutions and with the numerical solutions from the Godunov method in conjunction with the exact Riemann solver for the Euler equations with Mie-Grüneisen form of equations of state, such as the JWL and the C-C equations of state. The adaptive scheme is extended to second order and its empirical convergence rates are presented, verifying second order accuracy for smooth solutions. Through a suite of several tests problems in one and two space dimensions we illustrate the failure of conservative schemes and the capability of the methods of this paper to overcome the difficulties.

Estimation of Sonic Fatigue by Reduced-Order Finite Element Based Analyses

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2006-01-01

A computationally efficient, reduced-order method is presented for prediction of sonic fatigue of structures exhibiting geometrically nonlinear response. A procedure to determine the nonlinear modal stiffness using commercial finite element codes allows the coupled nonlinear equations of motion in physical degrees of freedom to be transformed to a smaller coupled system of equations in modal coordinates. The nonlinear modal system is first solved using a computationally light equivalent linearization solution to determine if the structure responds to the applied loading in a nonlinear fashion. If so, a higher fidelity numerical simulation in modal coordinates is undertaken to more accurately determine the nonlinear response. Comparisons of displacement and stress response obtained from the reduced-order analyses are made with results obtained from numerical simulation in physical degrees-of-freedom. Fatigue life predictions from nonlinear modal and physical simulations are made using the rainflow cycle counting method in a linear cumulative damage analysis. Results computed for a simple beam structure under a random acoustic loading demonstrate the effectiveness of the approach and compare favorably with results obtained from the solution in physical degrees-of-freedom.

Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow

NASA Astrophysics Data System (ADS)

Zheng, Lin; Zheng, Song; Zhai, Qinglan

2016-02-01

In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn-Hilliard equation which is solved in the frame work of LBE. The scalar convection-diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results.

Modeling Radionuclide Decay Chain Migration Using HYDROGEOCHEM

NASA Astrophysics Data System (ADS)

Lin, T. C.; Tsai, C. H.; Lai, K. H.; Chen, J. S.

2014-12-01

Nuclear technology has been employed for energy production for several decades. Although people receive many benefits from nuclear energy, there are inevitably environmental pollutions as well as human health threats posed by the radioactive materials releases from nuclear waste disposed in geological repositories or accidental releases of radionuclides from nuclear facilities. Theoretical studies have been undertaken to understand the transport of radionuclides in subsurface environments because that the radionuclide transport in groundwater is one of the main pathway in exposure scenarios for the intake of radionuclides. The radionuclide transport in groundwater can be predicted using analytical solution as well as numerical models. In this study, we simulate the transport of the radionuclide decay chain using HYDROGEOCHEM. The simulated results are verified against the analytical solution available in the literature. Excellent agreements between the numerical simulation and the analytical are observed for a wide spectrum of concentration. HYDROGECHEM is a useful tool assessing the ecological and environmental impact of the accidental radionuclide releases such as the Fukushima nuclear disaster where multiple radionuclides leaked through the reactor, subsequently contaminating the local groundwater and ocean seawater in the vicinity of the nuclear plant.

Limit Theorems and Their Relation to Solute Transport in Simulated Fractured Media

NASA Astrophysics Data System (ADS)

Reeves, D. M.; Benson, D. A.; Meerschaert, M. M.

2003-12-01

Solute particles that travel through fracture networks are subject to wide velocity variations along a restricted set of directions. This may result in super-Fickian dispersion along a few primary scaling directions. The fractional advection-dispersion equation (FADE), a modification of the original advection-dispersion equation in which a fractional derivative replaces the integer-order dispersion term, has the ability to model rapid, non-Gaussian solute transport. The FADE assumes that solute particle motions converge to either α -stable or operator stable densities, which are modeled by spatial fractional derivatives. In multiple dimensions, the multi-fractional dispersion derivative dictates the order and weight of differentiation in all directions, which correspond to the statistics of large particle motions in all directions. This study numerically investigates the presence of super- Fickian solute transport through simulated two-dimensional fracture networks. An ensemble of networks is gen

Analytic solution and pulse area theorem for three-level atoms

NASA Astrophysics Data System (ADS)

Shchedrin, Gavriil; O'Brien, Chris; Rostovtsev, Yuri; Scully, Marlan O.

2015-12-01

We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level V and Λ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.

Evidence for a scaling solution in cosmic-string evolution

NASA Technical Reports Server (NTRS)

Bennett, David P.; Bouchet, Francois R.

1988-01-01

Numerical simulations are used to study the most fundamental issue of cosmic-string evolution: the existence of a scaling solution. Strong evidence is found that a scaling solution does indeed exist. This justifies the main assumption on which the cosmic-string theories of galaxy formation is based. The main conclusion coincides with that of Albrecht and Turok (1985) but the results are not consistent with theirs. In fact, the results indicate that the details of string evolution are very different from the standard dogma.

Elegant Ince—Gaussian breathers in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2012-06-01

A novel class of optical breathers, called elegant Ince—Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schrödinger equation.

COUPLING OF CORONAL AND HELIOSPHERIC MAGNETOHYDRODYNAMIC MODELS: SOLUTION COMPARISONS AND VERIFICATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Merkin, V. G.; Lionello, R.; Linker, J.

2016-11-01

Two well-established magnetohydrodynamic (MHD) codes are coupled to model the solar corona and the inner heliosphere. The corona is simulated using the MHD algorithm outside a sphere (MAS) model. The Lyon–Fedder–Mobarry (LFM) model is used in the heliosphere. The interface between the models is placed in a spherical shell above the critical point and allows both models to work in either a rotating or an inertial frame. Numerical tests are presented examining the coupled model solutions from 20 to 50 solar radii. The heliospheric simulations are run with both LFM and the MAS extension into the heliosphere, and use themore » same polytropic coronal MAS solutions as the inner boundary condition. The coronal simulations are performed for idealized magnetic configurations, with an out-of-equilibrium flux rope inserted into an axisymmetric background, with and without including the solar rotation. The temporal evolution at the inner boundary of the LFM and MAS solutions is shown to be nearly identical, as are the steady-state background solutions, prior to the insertion of the flux rope. However, after the coronal mass ejection has propagated through the significant portion of the simulation domain, the heliospheric solutions diverge. Additional simulations with different resolution are then performed and show that the MAS heliospheric solutions approach those of LFM when run with progressively higher resolution. Following these detailed tests, a more realistic simulation driven by the thermodynamic coronal MAS is presented, which includes solar rotation and an azimuthally asymmetric background and extends to the Earth’s orbit.« less

Analytical theory of two-dimensional ring dark soliton in nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Chen, Wei; Wang, Qi; Shi, Jielong; Shen, Ming

2017-11-01

Completely stable two-dimensional ring dark soliton in nonlocal media with an arbitrary degree of nonlocality are investigated. The exact solution of the ring dark solitons is obtained with the variational method and a cylindrical nonlocal response function. The analytical results are confirmed by directly numerical simulations. We also analytically and numerically study the expansion dynamics of the gray ring dark solitons in detail.

Unsteady Flow Simulation: A Numerical Challenge

DTIC Science & Technology

2003-03-01

drive to convergence the numerical unsteady term. The time marching procedure is based on the approximate implicit Newton method for systems of non...computed through analytical derivatives of S. The linear system stemming from equation (3) is solved at each integration step by the same iterative method...significant reduction of memory usage, thanks to the reduced dimensions of the linear system matrix during the implicit marching of the solution. The

Avoiding numerical pitfalls in social force models

NASA Astrophysics Data System (ADS)

Köster, Gerta; Treml, Franz; Gödel, Marion

2013-06-01

The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.

Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Kok Foong; Patterson, Robert I.A.; Wagner, Wolfgang

2015-12-15

Graphical abstract: -- Highlights: •Problems concerning multi-compartment population balance equations are studied. •A class of fragmentation weight transfer functions is presented. •Three stochastic weighted algorithms are compared against the direct simulation algorithm. •The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate. •The algorithms are applied to a multi-dimensional granulation model. -- Abstract: This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. Themore » weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.« less

Time-periodic solutions of the Benjamin-Ono equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ambrose , D.M.; Wilkening, Jon

2008-04-01

We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one ofmore » the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.« less

Large eddy simulation of shock train in a convergent-divergent nozzle

NASA Astrophysics Data System (ADS)

Mousavi, Seyed Mahmood; Roohi, Ehsan

2014-12-01

This paper discusses the suitability of the Large Eddy Simulation (LES) turbulence modeling for the accurate simulation of the shock train phenomena in a convergent-divergent nozzle. To this aim, we selected an experimentally tested geometry and performed LES simulation for the same geometry. The structure and pressure recovery inside the shock train in the nozzle captured by LES model are compared with the experimental data, analytical expressions and numerical solutions obtained using various alternative turbulence models, including k-ɛ RNG, k-ω SST, and Reynolds stress model (RSM). Comparing with the experimental data, we observed that the LES solution not only predicts the "locations of the first shock" precisely, but also its results are quite accurate before and after the shock train. After validating the LES solution, we investigate the effects of the inlet total pressure on the shock train starting point and length. The effects of changes in the back pressure, nozzle inlet angle (NIA) and wall temperature on the behavior of the shock train are investigated by details.

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

NASA Technical Reports Server (NTRS)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

NASA Astrophysics Data System (ADS)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier-Stokes

NASA Astrophysics Data System (ADS)

Berselli, Luigi C.; Spirito, Stefano

2018-06-01

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier-Stokes-Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier-Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier-Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions.

Numerical Simulation of Black Holes

NASA Astrophysics Data System (ADS)

Teukolsky, Saul

2003-04-01

Einstein's equations of general relativity are prime candidates for numerical solution on supercomputers. There is some urgency in being able to carry out such simulations: Large-scale gravitational wave detectors are now coming on line, and the most important expected signals cannot be predicted except numerically. Problems involving black holes are perhaps the most interesting, yet also particularly challenging computationally. One difficulty is that inside a black hole there is a physical singularity that cannot be part of the computational domain. A second difficulty is the disparity in length scales between the size of the black hole and the wavelength of the gravitational radiation emitted. A third difficulty is that all existing methods of evolving black holes in three spatial dimensions are plagued by instabilities that prohibit long-term evolution. I will describe the ideas that are being introduced in numerical relativity to deal with these problems, and discuss the results of recent calculations of black hole collisions.

Multiphysics Simulation of Welding-Arc and Nozzle-Arc System: Mathematical-Model, Solution-Methodology and Validation

NASA Astrophysics Data System (ADS)

Pawar, Sumedh; Sharma, Atul

2018-01-01

This work presents mathematical model and solution methodology for a multiphysics engineering problem on arc formation during welding and inside a nozzle. A general-purpose commercial CFD solver ANSYS FLUENT 13.0.0 is used in this work. Arc formation involves strongly coupled gas dynamics and electro-dynamics, simulated by solution of coupled Navier-Stoke equations, Maxwell's equations and radiation heat-transfer equation. Validation of the present numerical methodology is demonstrated with an excellent agreement with the published results. The developed mathematical model and the user defined functions (UDFs) are independent of the geometry and are applicable to any system that involves arc-formation, in 2D axisymmetric coordinates system. The high-pressure flow of SF6 gas in the nozzle-arc system resembles arc chamber of SF6 gas circuit breaker; thus, this methodology can be extended to simulate arcing phenomenon during current interruption.

Temperature and solute-transport simulation in streamflow using a Lagrangian reference frame

USGS Publications Warehouse

Jobson, Harvey E.

1980-01-01

A computer program for simulating one-dimensional, unsteady temperature and solute transport in a river has been developed and documented for general use. The solution approach to the convective-diffusion equation uses a moving reference frame (Lagrangian) which greatly simplifies the mathematics of the solution procedure and dramatically reduces errors caused by numerical dispersion. The model documentation is presented as a series of four programs of increasing complexity. The conservative transport model can be used to route a single conservative substance. The simplified temperature model is used to predict water temperature in rivers when only temperature and windspeed data are available. The complete temperature model is highly accurate but requires rather complete meteorological data. Finally, the 10-parameter model can be used to route as many as 10 interacting constituents through a river reach. (USGS)

Parallel processing for nonlinear dynamics simulations of structures including rotating bladed-disk assemblies

NASA Technical Reports Server (NTRS)

Hsieh, Shang-Hsien

1993-01-01

The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system.

Development of multi-touch panel backlight system

NASA Astrophysics Data System (ADS)

Chomiczewski, J.; Długosz, M.; Godlewski, G.; Kochanowicz, M.

2013-10-01

The paper presents design, simulation analysis, and measurements of parameters of optical multi touch panel backlight system. Comparison of optical technology with commercially available solutions was also performed. The numerical simulation of laser based backlight system was made. The influence of the laser power, beam divergence, and placing reflective surfaces on the uniformity of illumination were examined. Optimal illumination system was used for further studies.

Enhanced verification test suite for physics simulation codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamm, James R.; Brock, Jerry S.; Brandon, Scott T.

2008-09-01

This document discusses problems with which to augment, in quantity and in quality, the existing tri-laboratory suite of verification problems used by Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), and Sandia National Laboratories (SNL). The purpose of verification analysis is demonstrate whether the numerical results of the discretization algorithms in physics and engineering simulation codes provide correct solutions of the corresponding continuum equations.

Implicit time accurate simulation of unsteady flow

NASA Astrophysics Data System (ADS)

van Buuren, René; Kuerten, Hans; Geurts, Bernard J.

2001-03-01

Implicit time integration was studied in the context of unsteady shock-boundary layer interaction flow. With an explicit second-order Runge-Kutta scheme, a reference solution to compare with the implicit second-order Crank-Nicolson scheme was determined. The time step in the explicit scheme is restricted by both temporal accuracy as well as stability requirements, whereas in the A-stable implicit scheme, the time step has to obey temporal resolution requirements and numerical convergence conditions. The non-linear discrete equations for each time step are solved iteratively by adding a pseudo-time derivative. The quasi-Newton approach is adopted and the linear systems that arise are approximately solved with a symmetric block Gauss-Seidel solver. As a guiding principle for properly setting numerical time integration parameters that yield an efficient time accurate capturing of the solution, the global error caused by the temporal integration is compared with the error resulting from the spatial discretization. Focus is on the sensitivity of properties of the solution in relation to the time step. Numerical simulations show that the time step needed for acceptable accuracy can be considerably larger than the explicit stability time step; typical ratios range from 20 to 80. At large time steps, convergence problems that are closely related to a highly complex structure of the basins of attraction of the iterative method may occur. Copyright

A numerical model for density-and-viscosity-dependent flows in two-dimensional variably saturated porous media

NASA Astrophysics Data System (ADS)

Boufadel, Michel C.; Suidan, Makram T.; Venosa, Albert D.

1999-04-01

We present a formulation for water flow and solute transport in two-dimensional variably saturated media that accounts for the effects of the solute on water density and viscosity. The governing equations are cast in a dimensionless form that depends on six dimensionless groups of parameters. These equations are discretized in space using the Galerkin finite element formulation and integrated in time using the backward Euler scheme with mass lumping. The modified Picard method is used to linearize the water flow equation. The resulting numerical model, the MARUN model, is verified by comparison to published numerical results. It is then used to investigate beach hydraulics at seawater concentration (about 30 g l -1) in the context of nutrients delivery for bioremediation of oil spills on beaches. Numerical simulations that we conducted in a rectangular section of a hypothetical beach revealed that buoyancy in the unsaturated zone is significant in soils that are fine textured, with low anisotropy ratio, and/or exhibiting low physical dispersion. In such situations, application of dissolved nutrients to a contaminated beach in a freshwater solution is superior to their application in a seawater solution. Concentration-engendered viscosity effects were negligible with respect to concentration-engendered density effects for the cases that we considered.

Breaking the GaN material limits with nanoscale vertical polarisation super junction structures: A simulation analysis

NASA Astrophysics Data System (ADS)

Unni, Vineet; Sankara Narayanan, E. M.

2017-04-01

This is the first report on the numerical analysis of the performance of nanoscale vertical superjunction structures based on impurity doping and an innovative approach that utilizes the polarisation properties inherent in III-V nitride semiconductors. Such nanoscale vertical polarisation super junction structures can be realized by employing a combination of epitaxial growth along the non-polar crystallographic axes of Wurtzite GaN and nanolithography-based processing techniques. Detailed numerical simulations clearly highlight the limitations of a doping based approach and the advantages of the proposed solution for breaking the unipolar one-dimensional material limits of GaN by orders of magnitude.

Numerical simulation of nonlinear feedback model of saccade generation circuit implemented in the LabView graphical programming language.

PubMed

Jackson, M E; Gnadt, J W

1999-03-01

The object-oriented graphical programming language LabView was used to implement the numerical solution to a computational model of saccade generation in primates. The computational model simulates the activity and connectivity of anatomical strictures known to be involved in saccadic eye movements. The LabView program provides a graphical user interface to the model that makes it easy to observe and modify the behavior of each element of the model. Essential elements of the source code of the LabView program are presented and explained. A copy of the model is available for download from the internet.

Implementing Parquet equations using HPX

NASA Astrophysics Data System (ADS)

Kellar, Samuel; Wagle, Bibek; Yang, Shuxiang; Tam, Ka-Ming; Kaiser, Hartmut; Moreno, Juana; Jarrell, Mark

A new C++ runtime system (HPX) enables simulations of complex systems to run more efficiently on parallel and heterogeneous systems. This increased efficiency allows for solutions to larger simulations of the parquet approximation for a system with impurities. The relevancy of the parquet equations depends upon the ability to solve systems which require long runs and large amounts of memory. These limitations, in addition to numerical complications arising from stability of the solutions, necessitate running on large distributed systems. As the computational resources trend towards the exascale and the limitations arising from computational resources vanish efficiency of large scale simulations becomes a focus. HPX facilitates efficient simulations through intelligent overlapping of computation and communication. Simulations such as the parquet equations which require the transfer of large amounts of data should benefit from HPX implementations. Supported by the the NSF EPSCoR Cooperative Agreement No. EPS-1003897 with additional support from the Louisiana Board of Regents.

Development of Numerical Tools for the Investigation of Plasma Detachment from Magnetic Nozzles

NASA Technical Reports Server (NTRS)

Sankaran, Kamesh; Polzin, Kurt A.

2007-01-01

A multidimensional numerical simulation framework aimed at investigating the process of plasma detachment from a magnetic nozzle is introduced. An existing numerical code based on a magnetohydrodynamic formulation of the plasma flow equations that accounts for various dispersive and dissipative processes in plasmas was significantly enhanced to allow for the modeling of axisymmetric domains containing three.dimensiunai momentum and magnetic flux vectors. A separate magnetostatic solver was used to simulate the applied magnetic field topologies found in various nozzle experiments. Numerical results from a magnetic diffusion test problem in which all three components of the magnetic field were present exhibit excellent quantitative agreement with the analytical solution, and the lack of numerical instabilities due to fluctuations in the value of del(raised dot)B indicate that the conservative MHD framework with dissipative effects is well-suited for multi-dimensional analysis of magnetic nozzles. Further studies will focus on modeling literature experiments both for the purpose of code validation and to extract physical insight regarding the mechanisms driving detachment.

Numerical Study of Outlet Boundary Conditions for Unsteady Turbulent Internal Flows Using the NCC

NASA Technical Reports Server (NTRS)

Liu, Nan-Suey; Shih, Tsan-Hsing

2009-01-01

This paper presents the results of studies on the outlet boundary conditions for turbulent internal flow simulations. Several outlet boundary conditions have been investigated by applying the National Combustion Code (NCC) to the configuration of a LM6000 single injector flame tube. First of all, very large eddy simulations (VLES) have been performed using the partially resolved numerical simulation (PRNS) approach, in which both the nonlinear and linear dynamic subscale models were employed. Secondly, unsteady Reynolds averaged Navier- Stokes (URANS) simulations have also been performed for the same configuration to investigate the effects of different outlet boundary conditions in the context of URANS. Thirdly, the possible role of the initial condition is inspected by using three different initial flow fields for both the PRNS/VLES simulation and the URANS simulation. The same grid is used for all the simulations and the number of mesh element is about 0.5 million. The main purpose of this study is to examine the long-time behavior of the solution as determined by the imposed outlet boundary conditions. For a particular simulation to be considered as successful under the given initial and boundary conditions, the solution must be sustainable in a physically meaningful manner over a sufficiently long period of time. The commonly used outlet boundary condition for steady Reynolds averaged Navier-Stokes (RANS) simulation is a fixed pressure at the outlet with all the other dependent variables being extrapolated from the interior. The results of the present study suggest that this is also workable for the URANS simulation of the LM6000 injector flame tube. However, it does not work for the PRNS/VLES simulation due to the unphysical reflections of the pressure disturbances at the outlet boundary. This undesirable situation can be practically alleviated by applying a simple unsteady convection equation for the pressure disturbances at the outlet boundary. The numerical results presented in this paper suggest that this unsteady convection of pressure disturbances at the outlet works very well for all the unsteady simulations (both PRNS/VLES and URANS) of the LM6000 single injector flame tube.

Numerical simulations of epitaxial growth process in MOVPE reactor as a tool for design of modern semiconductors for high power electronics

NASA Astrophysics Data System (ADS)

Skibinski, Jakub; Caban, Piotr; Wejrzanowski, Tomasz; Kurzydlowski, Krzysztof J.

2014-10-01

In the present study numerical simulations of epitaxial growth of gallium nitride in Metal Organic Vapor Phase Epitaxy reactor AIX-200/4RF-S is addressed. Epitaxial growth means crystal growth that progresses while inheriting the laminar structure and the orientation of substrate crystals. One of the technological problems is to obtain homogeneous growth rate over the main deposit area. Since there are many agents influencing reaction on crystal area such as temperature, pressure, gas flow or reactor geometry, it is difficult to design optimal process. According to the fact that it's impossible to determine experimentally the exact distribution of heat and mass transfer inside the reactor during crystal growth, modeling is the only solution to understand the process precisely. Numerical simulations allow to understand the epitaxial process by calculation of heat and mass transfer distribution during growth of gallium nitride. Including chemical reactions in numerical model allows to calculate the growth rate of the substrate and estimate the optimal process conditions for obtaining the most homogeneous product.

Collisional effects on the numerical recurrence in Vlasov-Poisson simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pezzi, Oreste; Valentini, Francesco; Camporeale, Enrico

The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here, we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456–1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through an Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used,more » an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.« less

Numerical simulation of tunneling through arbitrary potential barriers applied on MIM and MIIM rectenna diodes

NASA Astrophysics Data System (ADS)

Abdolkader, Tarek M.; Shaker, Ahmed; Alahmadi, A. N. M.

2018-07-01

With the continuous miniaturization of electronic devices, quantum-mechanical effects such as tunneling become more effective in many device applications. In this paper, a numerical simulation tool is developed under a MATLAB environment to calculate the tunneling probability and current through an arbitrary potential barrier comparing three different numerical techniques: the finite difference method, transfer matrix method, and transmission line method. For benchmarking, the tool is applied to many case studies such as the rectangular single barrier, rectangular double barrier, and continuous bell-shaped potential barrier, each compared to analytical solutions and giving the dependence of the error on the number of mesh points. In addition, a thorough study of the J ‑ V characteristics of MIM and MIIM diodes, used as rectifiers for rectenna solar cells, is presented and simulations are compared to experimental results showing satisfactory agreement. On the undergraduate level, the tool provides a deeper insight for students to compare numerical techniques used to solve various tunneling problems and helps students to choose a suitable technique for a certain application.

Fully dynamical simulation of central nuclear collisions.

PubMed

van der Schee, Wilke; Romatschke, Paul; Pratt, Scott

2013-11-27

We present a fully dynamical simulation of central nuclear collisions around midrapidity at LHC energies. Unlike previous treatments, we simulate all phases of the collision, including the equilibration of the system. For the simulation, we use numerical relativity solutions to anti-de Sitter space/conformal field theory for the preequilibrium stage, viscous hydrodynamics for the plasma equilibrium stage, and kinetic theory for the low-density hadronic stage. Our preequilibrium stage provides initial conditions for hydrodynamics, resulting in sizable radial flow. The resulting light particle spectra reproduce the measurements from the ALICE experiment at all transverse momenta.

Mathematical formulation and numerical simulation of bird flu infection process within a poultry farm

NASA Astrophysics Data System (ADS)

Putri, Arrival Rince; Nova, Tertia Delia; Watanabe, M.

2016-02-01

Bird flu infection processes within a poultry farm are formulated mathematically. A spatial effect is taken into account for the virus concentration with a diffusive term. An infection process is represented in terms of a traveling wave solutions. For a small removal rate, a singular perturbation analysis lead to existence of traveling wave solutions, that correspond to progressive infection in one direction.

Numerical Simulation of nZVI at the Field Scale

NASA Astrophysics Data System (ADS)

Chowdhury, A. I.; Krol, M.; Sleep, B. E.; O'Carroll, D. M.

2014-12-01

Nano-scale zero valent iron (nZVI) has been used at a number of contaminated sites over the last decade. At most of these sites, significant decreases in contaminant concentrations have resulted from the application of nZVI. However, limited work has been completed investigating nZVI mobility at the field-scale. In this study a three dimensional, three phase, finite difference numerical simulator (CompSim) was used to simulate nZVI and polymer transport in a variably saturated site. The model was able to accurately predict the field observed head data without parameter fitting. In addition, the numerical simulator estimated the amount of nZVI delivered to the saturated and unsaturated zones as well as the phase of nZVI (i.e., attached or aqueous phase). The simulation results showed that the injected slurry migrated radially outward from the injection well, and therefore nZVI transport was governed by injection velocity as well as viscosity of the injected solution. A suite of sensitivity analyses was performed to investigate the impact of different injection scenarios (e.g. different volume and injection rate) on nZVI migration. Simulation results showed that injection of a higher volume of nZVI delivered more iron particles at a given distance; however, not necessarily to a greater distance proportionate to the increase in volume. This study suggests that on-site synthesized nZVI particles are mobile in the subsurface and the numerical simulator can be a valuable tool for optimum design of nZVI applications.

A gradual update method for simulating the steady-state solution of stiff differential equations in metabolic circuits.

PubMed

Shiraishi, Emi; Maeda, Kazuhiro; Kurata, Hiroyuki

2009-02-01

Numerical simulation of differential equation systems plays a major role in the understanding of how metabolic network models generate particular cellular functions. On the other hand, the classical and technical problems for stiff differential equations still remain to be solved, while many elegant algorithms have been presented. To relax the stiffness problem, we propose new practical methods: the gradual update of differential-algebraic equations based on gradual application of the steady-state approximation to stiff differential equations, and the gradual update of the initial values in differential-algebraic equations. These empirical methods show a high efficiency for simulating the steady-state solutions for the stiff differential equations that existing solvers alone cannot solve. They are effective in extending the applicability of dynamic simulation to biochemical network models.

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

NASA Technical Reports Server (NTRS)

Molenaar, J.

1996-01-01

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Simulation of a Single-Element Lean-Direct Injection Combustor Using Arbitrary Polyhedral Mesh

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2012-01-01

This paper summarizes procedures of generating the arbitrary polyhedral mesh as well as presents sample results from its application to the numerical solution of a single-element LDI combustor using a preliminary version of the new OpenNCC.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

NASA Astrophysics Data System (ADS)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

Numerical Analysis of Shear Thickening Fluids for Blast Mitigation Applications

DTIC Science & Technology

2011-12-01

integrate with other types of physics simulation technologies ( ANSYS , 2011). One well-known product offered by ANSYS is the ANSYS CFX . The ANSYS CFD...centered. The ANSYS CFX solver uses coupled algebraic multigrid to achieve its solutions and its engineered scalability ensures a linear increase in CPU...on the user-defined distribution and size. As the numerical analysis focused on the behavior of each individual particle, the ANSYS CFX Rigid Body

Wave transience in a compressible atmosphere. I - Transient internal wave, mean-flow interaction. II - Transient equatorial waves in the quasi-biennial oscillation

NASA Technical Reports Server (NTRS)

Dunkerton, T. J.

1981-01-01

Analytical and numerical solutions are obtained in an approximate quasi-linear model, to describe the way in which vertically propagating waves give rise to mean flow accelerations in an atmosphere due to the effects of wave transience. These effects in turn result from compressibility and vertical group velocity feedback, and culminate in the spontaneous formation and descent of regions of strong mean wind shear. The numerical solutions display mean flow accelerations due to Kelvin waves in the equatorial stratosphere, with wave absorption altering the transience mechanism in such significant respects as causing the upper atmospheric mean flow acceleration to be very sensitive to the precise magnitude and distribution of the damping mechanisms. The numerical simulations of transient equatorial waves in the quasi-biennial oscillation are also considered.

Numerical modelling of bifurcation and localisation in cohesive-frictional materials

NASA Astrophysics Data System (ADS)

de Borst, René

1991-12-01

Methods are reviewed for analysing highly localised failure and bifurcation modes in discretised mechanical systems as typically arise in numerical simulations of failure in soils, rocks, metals and concrete. By the example of a plane-strain biaxial test it is shown that strain softening and lack of normality in elasto-plastic constitutive equations and the ensuing loss of ellipticity of the governing field equations cause a pathological mesh dependence of numerical solutions for such problems, thus rendering the results effectively meaningless. The need for introduction of higher-order continuum models is emphasised to remedy this shortcoming of the conventional approach. For one such a continuum model, namely the unconstrained Cosserat continuum, it is demonstrated that meaningful and convergent solutions (in the sense that a finite width of the localisation zone is computed upon mesh refinement) can be obtained.

Numerical modeling of zero-offset laboratory data in a strong topographic environment: results for a spectral-element method and a discretized Kirchhoff integral method

NASA Astrophysics Data System (ADS)

Favretto-Cristini, Nathalie; Tantsereva, Anastasiya; Cristini, Paul; Ursin, Bjørn; Komatitsch, Dimitri; Aizenberg, Arkady M.

2014-08-01

Accurate simulation of seismic wave propagation in complex geological structures is of particular interest nowadays. However conventional methods may fail to simulate realistic wavefields in environments with great and rapid structural changes, due for instance to the presence of shadow zones, diffractions and/or edge effects. Different methods, developed to improve seismic modeling, are typically tested on synthetic configurations against analytical solutions for simple canonical problems or reference methods, or via direct comparison with real data acquired in situ. Such approaches have limitations, especially if the propagation occurs in a complex environment with strong-contrast reflectors and surface irregularities, as it can be difficult to determine the method which gives the best approximation of the "real" solution, or to interpret the results obtained without an a priori knowledge of the geologic environment. An alternative approach for seismics consists in comparing the synthetic data with high-quality data collected in laboratory experiments under controlled conditions for a known configuration. In contrast with numerical experiments, laboratory data possess many of the characteristics of field data, as real waves propagate through models with no numerical approximations. We thus present a comparison of laboratory-scaled measurements of 3D zero-offset wave reflection of broadband pulses from a strong topographic environment immersed in a water tank with numerical data simulated by means of a spectral-element method and a discretized Kirchhoff integral method. The results indicate a good quantitative fit in terms of time arrivals and acceptable fit in amplitudes for all datasets.

Modeling solute transport in a heterogeneous unsaturated porous medium under dynamic boundary conditions on different spatial scales

NASA Astrophysics Data System (ADS)

Cremer, Clemens; Neuweiler, Insa; Bechtold, Michel

2013-04-01

Understanding transport of solutes/contaminants through unsaturated soil in the shallow subsurface is vital to assess groundwater quality, nutrient cycling or to plan remediation projects. Alternating precipitation and evaporation conditions causing upward and downward flux with differing flow paths, changes in saturation and related structural heterogeneity make the description of transport in the unsaturated zone near the soil-surface a complex problem. Preferential flow paths strongly depend, among other things, on the saturation of a medium. Recent studies (e.g. Bechtold et al., 2011) showed lateral flow and solute transport during evaporation conditions (upward flux) in vertically layered sand columns. Results revealed that during evaporation water and solute are redistributed laterally from coarse to fine media deeper in the soil, and towards zones of lowest hydraulic head near to the soil surface. These zones at the surface can be coarse or fine grained depending on saturation status and evaporation flux. However, if boundary conditions are reversed and precipitation is applied, the flow field is not reversed in the same manner, resulting in entirely different transport patterns for downward and upward flow. Therefore, considering net-flow rates alone is misleading when describing transport in the shallow unsaturated zone. In this contribution, we analyze transport of a solute in the shallow subsurface to assess effects resulting from the superposition of heterogeneous soil structures and dynamic flow conditions on various spatial scales. Two-dimensional numerical simulations of unsaturated flow and transport in heterogeneous porous media under changing boundary conditions are carried out using a finite-volume code coupled to a particle tracking algorithm to quantify solute transport and leaching rates. In order to validate numerical simulations, results are qualitatively compared to those of a physical experiment (Bechtold et al., 2011). Numerical simulations differ in lateral scale reaching from 0.2 m to 1.5 m, while the height of the domain is kept constant to 1.5m. Strong material heterogeneity is realized through vertical layers of coarse and fine sand. Both materials remain permanently under liquid-flow-dominated ('stage1') evaporation conditions. Spatial moments as well as the dilution index (Kitanidis, 1994) are used for quantification of transport behaviour. Results show that, while all simulations led to anomalous transport, infiltration-evaporation cycles lead to faster solute leaching rates than solely infiltration at the same net-infiltration rate in both homogeneous and heterogeneous media. Flow and transport-paths significantly differed between infiltration and evaporation, resulting in lateral water fluxes and hence lateral solute transport. Variation of the width of the model domain shows faster leaching rates for domains with small horizontal extent.

The stability of freak waves with regard to external impact and perturbation of initial data

NASA Astrophysics Data System (ADS)

Smirnova, Anna; Shamin, Roman

2014-05-01

We investigate solutions of the equations, describing freak waves, in perspective of stability with regard to external impact and perturbation of initial data. The modeling of freak waves is based on numerical solution of equations describing a non-stationary potential flow of the ideal fluid with a free surface. We consider the two-dimensional infinitely deep flow. For waves modeling we use the equations in conformal variables. The variant of these equations is offered in [1]. Mathematical correctness of these equations was discussed in [2]. These works establish the uniqueness of solutions, offer the effective numerical solution calculation methods, prove the numerical convergence of these methods. The important aspect of numerical modeling of freak waves is the stability of solutions, describing these waves. In this work we study the questions of stability with regards to external impact and perturbation of initial data. We showed the stability of freak waves numerical model, corresponding to the external impact. We performed series of computational experiments with various freak wave initial data and random external impact. This impact means the power density on free surface. In each experiment examine two waves: the wave that was formed by external impact and without one. In all the experiments we see the stability of equation`s solutions. The random external impact practically does not change the time of freak wave formation and its form. Later our work progresses to the investigation of solution's stability under perturbations of initial data. We take the initial data that provide a freak wave and get the numerical solution. In common we take the numerical solution of equation with perturbation of initial data. The computing experiments showed that the freak waves equations solutions are stable under perturbations of initial data.So we can make a conclusion that freak waves are stable relatively external perturbation and perturbation of initial data both. 1. Zakharov V.E., Dyachenko A.I., Vasilyev O.A. New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface// Eur. J.~Mech. B Fluids. 2002. V. 21. P. 283-291. 2. R.V. Shamin. Dynamics of an Ideal Liquid with a Free Surface in Conformal Variables // Journal of Mathematical Sciences, Vol. 160, No. 5, 2009. P. 537-678. 3. R.V. Shamin, V.E. Zakharov, A.I. Dyachenko. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y

Spurious Behavior of Shock-Capturing Methods: Problems Containing Stiff Source Terms and Discontinuities

NASA Technical Reports Server (NTRS)

Yee, Helen M. C.; Kotov, D. V.; Wang, Wei; Shu, Chi-Wang

2013-01-01

The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The smearing introduces a nonequilibrium state into the calculation. Thus as soon as a nonequilibrium value is introduced in this manner, the source term turns on and immediately restores equilibrium, while at the same time shifting the discontinuity to a cell boundary. The present study is to show that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Moreover, employing finite time steps and grid spacings that are below the standard Courant-Friedrich-Levy (CFL) limit on shockcapturing methods for compressible Euler and Navier-Stokes equations containing stiff reacting source terms and discontinuities reveals surprising counter-intuitive results. Unlike non-reacting flows, for stiff reactions with discontinuities, employing a time step and grid spacing that are below the CFL limit (based on the homogeneous part or non-reacting part of the governing equations) does not guarantee a correct solution of the chosen governing equations. Instead, depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The present investigation for three very different stiff system cases confirms some of the findings of Lafon & Yee (1996) and LeVeque & Yee (1990) for a model scalar PDE. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general.

Analysis of periodically excited non-linear systems by a parametric continuation technique

NASA Astrophysics Data System (ADS)

Padmanabhan, C.; Singh, R.

1995-07-01

The dynamic behavior and frequency response of harmonically excited piecewise linear and/or non-linear systems has been the subject of several recent investigations. Most of the prior studies employed harmonic balance or Galerkin schemes, piecewise linear techniques, analog simulation and/or direct numerical integration (digital simulation). Such techniques are somewhat limited in their ability to predict all of the dynamic characteristics, including bifurcations leading to the occurrence of unstable, subharmonic, quasi-periodic and/or chaotic solutions. To overcome this problem, a parametric continuation scheme, based on the shooting method, is applied specifically to a periodically excited piecewise linear/non-linear system, in order to improve understanding as well as to obtain the complete dynamic response. Parameter regions exhibiting bifurcations to harmonic, subharmonic or quasi-periodic solutions are obtained quite efficiently and systematically. Unlike other techniques, the proposed scheme can follow period-doubling bifurcations, and with some modifications obtain stable quasi-periodic solutions and their bifurcations. This knowledge is essential in establishing conditions for the occurrence of chaotic oscillations in any non-linear system. The method is first validated through the Duffing oscillator example, the solutions to which are also obtained by conventional one-term harmonic balance and perturbation methods. The second example deals with a clearance non-linearity problem for both harmonic and periodic excitations. Predictions from the proposed scheme match well with available analog simulation data as well as with multi-term harmonic balance results. Potential savings in computational time over direct numerical integration is demonstrated for some of the example cases. Also, this work has filled in some of the solution regimes for an impact pair, which were missed previously in the literature. Finally, one main limitation associated with the proposed procedure is discussed.

An innovative hybrid 3D analytic-numerical model for air breathing parallel channel counter-flow PEM fuel cells.

PubMed

Tavčar, Gregor; Katrašnik, Tomaž

2014-01-01

The parallel straight channel PEM fuel cell model presented in this paper extends the innovative hybrid 3D analytic-numerical (HAN) approach previously published by the authors with capabilities to address ternary diffusion systems and counter-flow configurations. The model's core principle is modelling species transport by obtaining a 2D analytic solution for species concentration distribution in the plane perpendicular to the cannel gas-flow and coupling consecutive 2D solutions by means of a 1D numerical pipe-flow model. Electrochemical and other nonlinear phenomena are coupled to the species transport by a routine that uses derivative approximation with prediction-iteration. The latter is also the core of the counter-flow computation algorithm. A HAN model of a laboratory test fuel cell is presented and evaluated against a professional 3D CFD simulation tool showing very good agreement between results of the presented model and those of the CFD simulation. Furthermore, high accuracy results are achieved at moderate computational times, which is owed to the semi-analytic nature and to the efficient computational coupling of electrochemical kinetics and species transport.

Multiphase flow modelling of volcanic ash particle settling in water using adaptive unstructured meshes

NASA Astrophysics Data System (ADS)

Jacobs, C. T.; Collins, G. S.; Piggott, M. D.; Kramer, S. C.; Wilson, C. R. G.

2013-02-01

Small-scale experiments of volcanic ash particle settling in water have demonstrated that ash particles can either settle slowly and individually, or rapidly and collectively as a gravitationally unstable ash-laden plume. This has important implications for the emplacement of tephra deposits on the seabed. Numerical modelling has the potential to extend the results of laboratory experiments to larger scales and explore the conditions under which plumes may form and persist, but many existing models are computationally restricted by the fixed mesh approaches that they employ. In contrast, this paper presents a new multiphase flow model that uses an adaptive unstructured mesh approach. As a simulation progresses, the mesh is optimized to focus numerical resolution in areas important to the dynamics and decrease it where it is not needed, thereby potentially reducing computational requirements. Model verification is performed using the method of manufactured solutions, which shows the correct solution convergence rates. Model validation and application considers 2-D simulations of plume formation in a water tank which replicate published laboratory experiments. The numerically predicted settling velocities for both individual particles and plumes, as well as instability behaviour, agree well with experimental data and observations. Plume settling is clearly hindered by the presence of a salinity gradient, and its influence must therefore be taken into account when considering particles in bodies of saline water. Furthermore, individual particles settle in the laminar flow regime while plume settling is shown (by plume Reynolds numbers greater than unity) to be in the turbulent flow regime, which has a significant impact on entrainment and settling rates. Mesh adaptivity maintains solution accuracy while providing a substantial reduction in computational requirements when compared to the same simulation performed using a fixed mesh, highlighting the benefits of an adaptive unstructured mesh approach.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations - Part 1: Nonhydrostatic inertia-gravity modes

NASA Astrophysics Data System (ADS)

Konor, Celal S.; Randall, David A.

2018-05-01

We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia-gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelastic equations that are discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of both horizontal grid spacing and vertical wavenumber are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by running linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined.Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone-resolving scales (with low horizontal wavenumbers). We conclude that, aided by nonhydrostatic effects, the Z and C grids become overall more accurate for cloud-resolving resolutions (with high horizontal wavenumbers) than for the cyclone-resolving scales.A companion paper, Part 2, discusses the impacts of the discretization on the Rossby modes on a midlatitude β plane.

High-order scheme for the source-sink term in a one-dimensional water temperature model

PubMed Central

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data. PMID:28264005

High-order scheme for the source-sink term in a one-dimensional water temperature model.

PubMed

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data.

Numerical Simulation of the Fluid-Structure Interaction of a Surface Effect Ship Bow Seal

NASA Astrophysics Data System (ADS)

Bloxom, Andrew L.

Numerical simulations of fluid-structure interaction (FSI) problems were performed in an effort to verify and validate a commercially available FSI tool. This tool uses an iterative partitioned coupling scheme between CD-adapco's STAR-CCM+ finite volume fluid solver and Simulia's Abaqus finite element structural solver to simulate the FSI response of a system. Preliminary verification and validation work (V&V) was carried out to understand the numerical behavior of the codes individually and together as a FSI tool. Verification and Validation work that was completed included code order verification of the respective fluid and structural solvers with Couette-Poiseuille flow and Euler-Bernoulli beam theory. These results confirmed the 2 nd order accuracy of the spatial discretizations used. Following that, a mixture of solution verifications and model calibrations was performed with the inclusion of the physics models implemented in the solution of the FSI problems. Solution verifications were completed for fluid and structural stand-alone models as well as for the coupled FSI solutions. These results re-confirmed the spatial order of accuracy but for more complex flows and physics models as well as the order of accuracy of the temporal discretizations. In lieu of a good material definition, model calibration is performed to reproduce the experimental results. This work used model calibration for both instances of hyperelastic materials which were presented in the literature as validation cases because these materials were defined as linear elastic. Calibrated, three dimensional models of the bow seal on the University of Michigan bow seal test platform showed the ability to reproduce the experimental results qualitatively through averaging of the forces and seal displacements. These simulations represent the only current 3D results for this case. One significant result of this study is the ability to visualize the flow around the seal and to directly measure the seal resistances at varying cushion pressures, seal immersions, forward speeds, and different seal materials. SES design analysis could greatly benefit from the inclusion of flexible seals in simulations, and this work is a positive step in that direction. In future work, the inclusion of more complex seal geometries and contact will further enhance the capability of this tool.

Ocean modelling on the CYBER 205 at GFDL

NASA Technical Reports Server (NTRS)

Cox, M.

1984-01-01

At the Geophysical Fluid Dynamics Laboratory, research is carried out for the purpose of understanding various aspects of climate, such as its variability, predictability, stability and sensitivity. The atmosphere and oceans are modelled mathematically and their phenomenology studied by computer simulation methods. The present state-of-the-art in the computer simulation of large scale oceans on the CYBER 205 is discussed. While atmospheric modelling differs in some aspects, the basic approach used is similar. The equations of the ocean model are presented along with a short description of the numerical techniques used to find their solution. Computational considerations and a typical solution are presented in section 4.

CAG12 - A CSCM based procedure for flow of an equilibrium chemically reacting gas

NASA Technical Reports Server (NTRS)

Green, M. J.; Davy, W. C.; Lombard, C. K.

1985-01-01

The Conservative Supra Characteristic Method (CSCM), an implicit upwind Navier-Stokes algorithm, is extended to the numerical simulation of flows in chemical equilibrium. The resulting computer code known as Chemistry and Gasdynamics Implicit - Version 2 (CAG12) is described. First-order accurate results are presented for inviscid and viscous Mach 20 flows of air past a hemisphere-cylinder. The solution procedure captures the bow shock in a chemically reacting gas, a technique that is needed for simulating high altitude, rarefied flows. In an initial effort to validate the code, the inviscid results are compared with published gasdynamic and chemistry solutions and satisfactorily agreement is obtained.

A 2-D numerical simulation study on longitudinal solute transport and longitudinal dispersion coefficient

NASA Astrophysics Data System (ADS)

Zhang, Wei

2011-07-01

The longitudinal dispersion coefficient, DL, is a fundamental parameter of longitudinal solute transport models: the advection-dispersion (AD) model and various deadzone models. Since DL cannot be measured directly, and since its calibration using tracer test data is quite expensive and not always available, researchers have developed various methods, theoretical or empirical, for estimating DL by easier available cross-sectional hydraulic measurements (i.e., the transverse velocity profile, etc.). However, for known and unknown reasons, DL cannot be satisfactorily predicted using these theoretical/empirical formulae. Either there is very large prediction error for theoretical methods, or there is a lack of generality for the empirical formulae. Here, numerical experiments using Mike21, a software package that implements one of the most rigorous two-dimensional hydrodynamic and solute transport equations, for longitudinal solute transport in hypothetical streams, are presented. An analysis of the evolution of simulated solute clouds indicates that the two fundamental assumptions in Fischer's longitudinal transport analysis may be not reasonable. The transverse solute concentration distribution, and hence the longitudinal transport appears to be controlled by a dimensionless number ?, where Q is the average volumetric flowrate, Dt is a cross-sectional average transverse dispersion coefficient, and W is channel flow width. A simple empirical ? relationship may be established. Analysis and a revision of Fischer's theoretical formula suggest that ɛ influences the efficiency of transverse mixing and hence has restraining effect on longitudinal spreading. The findings presented here would improve and expand our understanding of longitudinal solute transport in open channel flow.

Modeling of long range frequency sweeping for energetic particle modes

NASA Astrophysics Data System (ADS)

Nyqvist, R. M.; Breizman, B. N.

2013-04-01

Long range frequency sweeping events are simulated numerically within a one-dimensional, electrostatic bump-on-tail model with fast particle sources and collisions. The numerical solution accounts for fast particle trapping and detrapping in an evolving wave field with a fixed wavelength, and it includes three distinct collisions operators: Drag (dynamical friction on the background electrons), Krook-type collisions, and velocity space diffusion. The effects of particle trapping and diffusion on the evolution of holes and clumps are investigated, and the occurrence of non-monotonic (hooked) frequency sweeping and asymptotically steady holes is discussed. The presented solution constitutes a step towards predictive modeling of frequency sweeping events in more realistic geometries.

Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

NASA Astrophysics Data System (ADS)

Priya, B. Ganesh; Muthukumar, P.

2018-02-01

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

Numerical simulation of the interaction between a flowfield and chemical reaction on premixed pulsed jet combustion

NASA Astrophysics Data System (ADS)

Hishida, Manabu; Hayashi, A. Koichi

1992-12-01

Pulsed Jet Combustion (PJC) is numerically simulated using time-dependent, axisymmetric, full Navier-Stokes equations with the mass, momentum, energy, and species conservation equations for a hydrogen-air mixture. A hydrogen-air reaction mechanism is modeled by nine species and nineteen elementary forward and backward reactions to evaluate the effect of the chemical reactions accurately. A point implicit method with the Harten and Yee's non-MUSCL (Monotone Upstream-centerd Schemes for Conservation Laws) modified-flux type TVD (Total Variation Diminishing) scheme is applied to deal with the stiff partial differential equations. Furthermore, a zonal method making use of the Fortified Solution Algorithm (FSA) is applied to simulate the phenomena in the complicated shape of the sub-chamber. The numerical result shows that flames propagating in the sub-chamber interact with pressure waves and are deformed to be wrinkled like a 'tulip' flame and a jet passed through the orifice changes its mass flux quasi-periodically.

Large eddy simulation modeling of particle-laden flows in complex terrain

NASA Astrophysics Data System (ADS)

Salesky, S.; Giometto, M. G.; Chamecki, M.; Lehning, M.; Parlange, M. B.

2017-12-01

The transport, deposition, and erosion of heavy particles over complex terrain in the atmospheric boundary layer is an important process for hydrology, air quality forecasting, biology, and geomorphology. However, in situ observations can be challenging in complex terrain due to spatial heterogeneity. Furthermore, there is a need to develop numerical tools that can accurately represent the physics of these multiphase flows over complex surfaces. We present a new numerical approach to accurately model the transport and deposition of heavy particles in complex terrain using large eddy simulation (LES). Particle transport is represented through solution of the advection-diffusion equation including terms that represent gravitational settling and inertia. The particle conservation equation is discretized in a cut-cell finite volume framework in order to accurately enforce mass conservation. Simulation results will be validated with experimental data, and numerical considerations required to enforce boundary conditions at the surface will be discussed. Applications will be presented in the context of snow deposition and transport, as well as urban dispersion.

Numerical Simulation of a High-Lift Configuration with Embedded Fluidic Actuators

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Casalino, Damiano; Lin, John C.; Appelbaum, Jason

2014-01-01

Numerical simulations have been performed for a vertical tail configuration with deflected rudder. The suction surface of the main element of this configuration is embedded with an array of 32 fluidic actuators that produce oscillating sweeping jets. Such oscillating jets have been found to be very effective for flow control applications in the past. In the current paper, a high-fidelity computational fluid dynamics (CFD) code known as the PowerFLOW(Registered TradeMark) code is used to simulate the entire flow field associated with this configuration, including the flow inside the actuators. The computed results for the surface pressure and integrated forces compare favorably with measured data. In addition, numerical solutions predict the correct trends in forces with active flow control compared to the no control case. Effect of varying yaw and rudder deflection angles are also presented. In addition, computations have been performed at a higher Reynolds number to assess the performance of fluidic actuators at flight conditions.

The Use of Input-Output Control System Analysis for Sustainable Development of Multivariable Environmental Systems

NASA Astrophysics Data System (ADS)

Koliopoulos, T. C.; Koliopoulou, G.

2007-10-01

We present an input-output solution for simulating the associated behavior and optimized physical needs of an environmental system. The simulations and numerical analysis determined the accurate boundary loads and areas that were required to interact for the proper physical operation of a complicated environmental system. A case study was conducted to simulate the optimum balance of an environmental system based on an artificial intelligent multi-interacting input-output numerical scheme. The numerical results were focused on probable further environmental management techniques, with the objective of minimizing any risks and associated environmental impact to protect the quality of public health and the environment. Our conclusions allowed us to minimize the associated risks, focusing on probable cases in an emergency to protect the surrounded anthropogenic or natural environment. Therefore, the lining magnitude could be determined for any useful associated technical works to support the environmental system under examination, taking into account its particular boundary necessities and constraints.

On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

NASA Astrophysics Data System (ADS)

Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

2017-01-01

In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

Numerical simulation of electrophoresis separation processes

NASA Technical Reports Server (NTRS)

Ganjoo, D. K.; Tezduyar, T. E.

1986-01-01

A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization, and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which consider temporal as well as spatial discretization, provide improved solutions. Electrophoresis, which involves the motion of charged entities under the influence of an applied electric field, is governed by equations similiar to those encountered in fluid flow problems, i.e., transient convection-diffusion equations. Test problems are solved in electrophoresis and fluid flow. The results obtained are satisfactory. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and the Navier-Stokes equations.

PROCESS SIMULATION OF COLD PRESSING OF ARMSTRONG CP-Ti POWDERS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sabau, Adrian S; Gorti, Sarma B; Peter, William H

A computational methodology is presented for the process simulation of cold pressing of Armstrong CP-Ti Powders. The computational model was implemented in the commercial finite element program ABAQUSTM. Since the powder deformation and consolidation is governed by specific pressure-dependent constitutive equations, several solution algorithms were developed for the ABAQUS user material subroutine, UMAT. The solution algorithms were developed for computing the plastic strain increments based on an implicit integration of the nonlinear yield function, flow rule, and hardening equations that describe the evolution of the state variables. Since ABAQUS requires the use of a full Newton-Raphson algorithm for the stress-strainmore » equations, an algorithm for obtaining the tangent/linearization moduli, which is consistent with the return-mapping algorithm, also was developed. Numerical simulation results are presented for the cold compaction of the Ti powders. Several simulations were conducted for cylindrical samples with different aspect ratios. The numerical simulation results showed that for the disk samples, the minimum von Mises stress was approximately half than its maximum value. The hydrostatic stress distribution exhibits a variation smaller than that of the von Mises stress. It was found that for the disk and cylinder samples the minimum hydrostatic stresses were approximately 23 and 50% less than its maximum value, respectively. It was also found that the minimum density was noticeably affected by the sample height.« less

Development of a methodology to compute solvation free energies on the basis of the theory of energy representation for solutions represented with a polarizable force field.

PubMed

Suzuoka, Daiki; Takahashi, Hideaki; Ishiyama, Tatsuya; Morita, Akihiro

2012-12-07

We have developed a method of molecular simulations utilizing a polarizable force field in combination with the theory of energy representation (ER) for the purpose of establishing an efficient and accurate methodology to compute solvation free energies. The standard version of the ER method is, however, based on the assumption that the solute-solvent interaction is pairwise additive for its construction. A crucial step in the present method is to introduce an intermediate state in the solvation process to treat separately the many-body interaction associated with the polarizable model. The intermediate state is chosen so that the solute-solvent interaction can be formally written in the pairwise form, though the solvent molecules are interacting with each other with polarizable charges dependent on the solvent configuration. It is, then, possible to extract the free energy contribution δμ due to the many-body interaction between solute and solvent from the total solvation free energy Δμ. It is shown that the free energy δμ can be computed by an extension of the recent development implemented in quantum mechanical∕molecular mechanical simulations. To assess the numerical robustness of the approach, we computed the solvation free energies of a water and a methanol molecule in water solvent, where two paths for the solvation processes were examined by introducing different intermediate states. The solvation free energies of a water molecule associated with the two paths were obtained as -5.3 and -5.8 kcal∕mol. Those of a methanol molecule were determined as -3.5 and -3.7 kcal∕mol. These results of the ER simulations were also compared with those computed by a numerically exact approach. It was demonstrated that the present approach produces the solvation free energies in comparable accuracies to simulations of thermodynamic integration (TI) method within a tenth of computational time used for the TI simulations.

Simulation and analysis of airborne antenna radiation patterns

NASA Technical Reports Server (NTRS)

Kim, J. J.; Burnside, Walter D.

1984-01-01

The objective is to develop an accurate and efficient analytic solution for predicting high frequency radiation patterns of fuselage-mounted airborne antennas. This is an analytic study of airborne antenna patterns using the Uniform Geometrical Theory of Diffraction (UTD). The aircraft is modeled in its most basic form so that the solution is applicable to general-type aircraft. The fuselage is modeled as a perfectly conducting composite ellipsoid; whereas, the wings, stabilizers, nose, fuel tanks, and engines, are simulated as perfectly conducting flat plates that can be attached to the fuselage and/or to each other. The composite-ellipsoid fuselage model is necessary to successfully simulate the wide variety of real world fuselage shapes. Since the antenna is mounted on the fuselage, it has a dominant effect on the resulting radiation pattern so it must be simulated accurately, especially near the antenna. Various radiation patterns are calculated for commercial, private, and military aircraft, and the Space Shuttle Orbiter. The application of this solution to numerous practical airborne antenna problems illustrates its versatility and design capability. In most cases, the solution accuracy is verified by the comparisons between the calculated and measured data.

Exact and approximate solutions for transient squeezing flow

NASA Astrophysics Data System (ADS)

Lang, Ji; Santhanam, Sridhar; Wu, Qianhong

2017-10-01

In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature and will have a broad impact on industrial and biomedical applications.

Development of the T+M coupled flow–geomechanical simulator to describe fracture propagation and coupled flow–thermal–geomechanical processes in tight/shale gas systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Jihoon; Moridis, George J.

2013-10-01

We developed a hydraulic fracturing simulator by coupling a flow simulator to a geomechanics code, namely T+M simulator. Modeling of the vertical fracture development involves continuous updating of the boundary conditions and of the data connectivity, based on the finite element method for geomechanics. The T+M simulator can model the initial fracture development during the hydraulic fracturing operations, after which the domain description changes from single continuum to double or multiple continua in order to rigorously model both flow and geomechanics for fracture-rock matrix systems. The T+H simulator provides two-way coupling between fluid-heat flow and geomechanics, accounting for thermoporomechanics, treatsmore » nonlinear permeability and geomechanical moduli explicitly, and dynamically tracks changes in the fracture(s) and in the pore volume. We also fully accounts for leak-off in all directions during hydraulic fracturing. We first validate the T+M simulator, matching numerical solutions with the analytical solutions for poromechanical effects, static fractures, and fracture propagations. Then, from numerical simulation of various cases of the planar fracture propagation, shear failure can limit the vertical fracture propagation of tensile failure, because of leak-off into the reservoirs. Slow injection causes more leak-off, compared with fast injection, when the same amount of fluid is injected. Changes in initial total stress and contributions of shear effective stress to tensile failure can also affect formation of the fractured areas, and the geomechanical responses are still well-posed.« less

Analysis of groundwater flow and stream depletion in L-shaped fluvial aquifers

NASA Astrophysics Data System (ADS)

Lin, Chao-Chih; Chang, Ya-Chi; Yeh, Hund-Der

2018-04-01

Understanding the head distribution in aquifers is crucial for the evaluation of groundwater resources. This article develops a model for describing flow induced by pumping in an L-shaped fluvial aquifer bounded by impermeable bedrocks and two nearly fully penetrating streams. A similar scenario for numerical studies was reported in Kihm et al. (2007). The water level of the streams is assumed to be linearly varying with distance. The aquifer is divided into two subregions and the continuity conditions of the hydraulic head and flux are imposed at the interface of the subregions. The steady-state solution describing the head distribution for the model without pumping is first developed by the method of separation of variables. The transient solution for the head distribution induced by pumping is then derived based on the steady-state solution as initial condition and the methods of finite Fourier transform and Laplace transform. Moreover, the solution for stream depletion rate (SDR) from each of the two streams is also developed based on the head solution and Darcy's law. Both head and SDR solutions in the real time domain are obtained by a numerical inversion scheme called the Stehfest algorithm. The software MODFLOW is chosen to compare with the proposed head solution for the L-shaped aquifer. The steady-state and transient head distributions within the L-shaped aquifer predicted by the present solution are compared with the numerical simulations and measurement data presented in Kihm et al. (2007).

Numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Calini, A.; Schober, C. M.

2013-09-01

In this article we present the results of a broad numerical investigation on the stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, specifically the one- and two-mode breathers for an unstable plane wave, which are frequently used to model rogue waves. The numerical experiments involve large ensembles of perturbed initial data for six typical random perturbations. Ensemble estimates of the "closeness", A(t), of the perturbed solution to an element of the respective unperturbed family indicate that the only neutrally stable breathers are the ones of maximal dimension, that is: given an unstable background with N unstable modes, the only neutrally stable breathers are the N-dimensional ones (obtained as a superimposition of N simple breathers via iterated Backlund transformations). Conversely, breathers which are not fully saturated are sensitive to noisy environments and are unstable. Interestingly, A(t) is smallest for the coalesced two-mode breather indicating the coalesced case may be the most robust two-mode breather in a laboratory setting. The numerical simulations confirm and provide a realistic realization of the stability behavior established analytically by the authors.