Numerical modelling of nonlinear full-wave acoustic propagation

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

Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx

2015-10-28

The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on amore » GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.« less

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

USGS Publications Warehouse

Franz, Delbert D.; Melching, Charles S.

1997-01-01

The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The accuracy and convergence of the numerical routines in the model are demonstrated for the case of laboratory measurements of unsteady flow in a sewer pipe. Verification of the routines in the model for field data on the Fox River in northeastern Illinois also is briefly discussed. The basic principles of unsteady-flow modeling and the relation between steady flow and unsteady flow are presented. Assumptions and the limitations of the model also are presented. The schematization of the stream system and the conversion of the physical characteristics of the stream reaches and a wide range of special features into function tables for model applications are described. The modified dynamic-wave equation used in FEQ for unsteady flow in curvilinear channels with drag on minor hydraulic structures and channel constrictions determined from an equivalent energy slope is developed. The matrix equation relating flows and depths at computational nodes throughout the stream system by the continuity (conservation of mass) and modified dynamic-wave equations is illustrated for four sequential examples. The solution of the matrix equation by Newton's method is discussed. Finally, the input for FEQ and the error messages and warnings issued are presented.

Conservation laws and conserved quantities for (1+1)D linearized Boussinesq equations

NASA Astrophysics Data System (ADS)

Carvalho, Cindy; Harley, Charis

2017-05-01

Conservation laws and physical conserved quantities for the (1+1)D linearized Boussinesq equations at a constant water depth are presented. These equations describe incompressible, inviscid, irrotational fluid flow in the form of a non steady solitary wave. A systematic multiplier approach is used to obtain the conservation laws of the system of third order partial differential equations (PDEs) in dimensional form. Physical conserved quantities are derived by integrating the conservation laws in the direction of wave propagation and imposing decaying boundary conditions in the horizontal direction. One of these is a newly discovered conserved quantity which relates to an energy flux density.

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

NASA Astrophysics Data System (ADS)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

Nonlinear and dissipative constitutive equations for coupled first-order acoustic field equations that are consistent with the generalized Westervelt equation

NASA Astrophysics Data System (ADS)

Verweij, Martin D.; Huijssen, Jacob

2006-05-01

In diagnostic medical ultrasound, it has become increasingly important to evaluate the nonlinear field of an acoustic beam that propagates in a weakly nonlinear, dissipative medium and that is steered off-axis up to very wide angles. In this case, computations cannot be based on the widely used KZK equation since it applies only to small angles. To benefit from successful computational schemes from elastodynamics and electromagnetics, we propose to use two first-order acoustic field equations, accompanied by two constitutive equations, as an alternative basis. This formulation quite naturally results in the contrast source formalism, makes a clear distinction between fundamental conservation laws and medium behavior, and allows for a straightforward inclusion of any medium inhomogenities. This paper is concerned with the derivation of relevant constitutive equations. We take a pragmatic approach and aim to find those constitutive equations that represent the same medium as implicitly described by the recognized, full wave, nonlinear equations such as the generalized Westervelt equation. We will show how this is achieved by considering the nonlinear case without attenuation, the linear case with attenuation, and the nonlinear case with attenuation. As a result we will obtain surprisingly simple constitutive equations for the full wave case.

On the conservation laws of Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

San, Sait; Yaşar, Emrullah

2015-05-01

In this study, the nonlocal conservation theorem and multiplier approach are performed on the 1 + 1 dimensional Derrida-Lebowitz-Speer-Spohn (DLSS) equation which arises in quantum semi conductor theory. We obtain local conservation laws by using the both methods. Furthermore by utilizing the relationship between conservation laws and Lie point symmetries, the DLSS equation is reduced to third order ordinary differential equation.

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

Cheviakov, Alexei F., E-mail: chevaikov@math.usask.ca

Partial differential equations of the form divN=0, N{sub t}+curl M=0 involving two vector functions in R{sup 3} depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R{sup 4}(t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations,more » it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented.« less

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

NASA Astrophysics Data System (ADS)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-11-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.

Conservation properties of numerical integration methods for systems of ordinary differential equations

NASA Technical Reports Server (NTRS)

Rosenbaum, J. S.

1976-01-01

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Boundary Conditions for Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Rosenhaus, V.; Bruzón, M. S.; Gandarias, M. L.

2016-12-01

Regular soliton equations (KdV, sine-Gordon, NLS) are known to possess infinite sets of local conservation laws. Some other classes of nonlinear PDE possess infinite-dimensional symmetries parametrized by arbitrary functions of independent or dependent variables; among them are Zabolotskaya-Khokhlov, Kadomtsev-Petviashvili, Davey-Stewartson equations and Born-Infeld equation. Boundary conditions were shown to play an important role for the existence of local conservation laws associated with infinite-dimensional symmetries. In this paper, we analyze boundary conditions for the infinite conserved densities of regular soliton equations: KdV, potential KdV, Sine-Gordon equation, and nonlinear Schrödinger equation, and compare them with boundary conditions for the conserved densities obtained from infinite-dimensional symmetries with arbitrary functions of independent and dependent variables.

Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Rui, Wenjuan; Zhang, Xiangzhi

2016-05-01

This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

Conservation-form equations of unsteady open-channel flow

USGS Publications Warehouse

Lai, C.; Baltzer, R.A.; Schaffranek, R.W.

2002-01-01

The unsteady open-channel flow equations are typically expressed in a variety of forms due to the imposition of differing assumptions, use of varied dependent variables, and inclusion of different source/sink terms. Questions often arise as to whether a particular equation set is expressed in a form consistent with the conservation-law definition. The concept of conservation form is developed to clarify the meaning mathematically. Six sets of unsteady-flow equations typically used in engineering practice are presented and their conservation properties are identified and discussed. Results of the theoretical development and analysis of the equations are substantiated in a set of numerical experiments conducted using alternate equation forms. Findings of these analytical and numerical efforts demonstrate that the choice of dependent variable is the fundamental factor determining the nature of the conservation properties of any particular equation form.

Mechanical balance laws for fully nonlinear and weakly dispersive water waves

NASA Astrophysics Data System (ADS)

Kalisch, Henrik; Khorsand, Zahra; Mitsotakis, Dimitrios

2016-10-01

The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is known to describe accurately the wave motion at the surface of an incompressible inviscid fluid in the case when the fluid flow is irrotational and two-dimensional. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence of the present analysis is that the energy loss appearing in the shallow-water theory of undular bores is fully compensated by the emergence of oscillations behind the bore front. The situation is analyzed numerically by approximating solutions of the Serre-Green-Naghdi equations using a finite-element discretization coupled with an adaptive Runge-Kutta time integration scheme, and it is found that the energy is indeed conserved nearly to machine precision. As a second application, the shoaling of solitary waves on a plane beach is analyzed. It appears that the Serre-Green-Naghdi equations are capable of predicting both the shape of the free surface and the evolution of kinetic and potential energy with good accuracy in the early stages of shoaling.

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.

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

NASA Technical Reports Server (NTRS)

Barth, T. J.; Steger, J. L.

1985-01-01

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Some aspects of steam-water flow simulation in geothermal wells

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

Shulyupin, Alexander N.

1996-01-24

Actual aspects of steam-water simulation in geothermal wells are considered: necessary quality of a simulator, flow regimes, mass conservation equation, momentum conservation equation, energy conservation equation and condition equations. Shortcomings of traditional hydraulic approach are noted. Main questions of simulator development by the hydraulic approach are considered. New possibilities of a simulation with the structure approach employment are noted.

On a new class of completely integrable nonlinear wave equations. I. Infinitely many conservation laws

NASA Astrophysics Data System (ADS)

Nutku, Y.

1985-06-01

We point out a class of nonlinear wave equations which admit infinitely many conserved quantities. These equations are characterized by a pair of exact one-forms. The implication that they are closed gives rise to equations, the characteristics and Riemann invariants of which are readily obtained. The construction of the conservation laws requires the solution of a linear second-order equation which can be reduced to canonical form using the Riemann invariants. The hodograph transformation results in a similar linear equation. We discuss also the symplectic structure and Bäcklund transformations associated with these equations.

Conservation laws and symmetries of a generalized Kawahara equation

NASA Astrophysics Data System (ADS)

Gandarias, Maria Luz; Rosa, Maria; Recio, Elena; Anco, Stephen

2017-06-01

The generalized Kawahara equation ut = a(t)uxxxxx + b(t)uxxx + c(t) f (u)ux appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation ut = αuux + βu2ux + γuxxx + μuxxxxx. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether's theorem using a potential formulation.

Progress Report on SAM Reduced-Order Model Development for Thermal Stratification and Mixing during Reactor Transients

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

Hu, R.

This report documents the initial progress on the reduced-order flow model developments in SAM for thermal stratification and mixing modeling. Two different modeling approaches are pursued. The first one is based on one-dimensional fluid equations with additional terms accounting for the thermal mixing from both flow circulations and turbulent mixing. The second approach is based on three-dimensional coarse-grid CFD approach, in which the full three-dimensional fluid conservation equations are modeled with closure models to account for the effects of turbulence.

Well-posedness, linear perturbations, and mass conservation for the axisymmetric Einstein equations

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

Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, FaMAF, Universidad Nacional de Cordoba, Instituto de Fisica Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria

2010-02-15

For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides a nonlinear control of the variables along the whole evolution. In this gauge, Einstein equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. As a first step in analyzing this system of equations we study linear perturbations on a flat background. We prove that the linear equations reduce to a very simple system of equations which provide, thoughmore » the mass formula, useful insight into the structure of the full system. However, the singular behavior of the coefficients at the axis makes the study of this linear system difficult from the analytical point of view. In order to understand the behavior of the solutions, we study the numerical evolution of them. We provide strong numerical evidence that the system is well-posed and that its solutions have the expected behavior. Finally, this linear system allows us to formulate a model problem which is physically interesting in itself, since it is connected with the linear stability of black hole solutions in axial symmetry. This model can contribute significantly to solve the nonlinear problem and at the same time it appears to be tractable.« less

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.

2003-01-01

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham-Broer-Kaup-Like Equations

NASA Astrophysics Data System (ADS)

Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian

2017-03-01

In this article, a generalised Whitham-Broer-Kaup-Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham-Broer-Kaup-Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert

2018-07-01

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method

NASA Astrophysics Data System (ADS)

Rasin, Alexander G.

2010-06-01

The application of the Gardner method for the generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely Bäcklund transformations and initial conservation laws, follows from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for the generation of symmetries is developed and applied to the discrete Korteweg-de Vries equation. It can also be applied to all the other ABS equations.

Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation

NASA Astrophysics Data System (ADS)

de la Rosa, R.; Gandarias, M. L.; Bruzón, M. S.

2016-11-01

In this paper we study the generalized variable-coefficient Gardner equations of the form ut + A(t) unux + C(t) u2nux + B(t) uxxx + Q(t) u = 0 . This class broadens out many other equations previously considered: Johnpillai and Khalique (2010), Molati and Ramollo (2012) and Vaneeva et al. (2015). The use of the equivalence group of this class allows us to perform an exhaustive study and a simple and clear formulation of the results. Some conservation laws are derived for the nonlinearly self-adjoint equations by using a general theorem on conservation laws. We also construct conservation laws by applying the multipliers method.

Properties of finite difference models of non-linear conservative oscillators

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1988-01-01

Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

A convergent series expansion for hyperbolic systems of conservation laws

NASA Technical Reports Server (NTRS)

Harabetian, E.

1985-01-01

The discontinuities piecewise analytic initial value problem for a wide class of conservation laws is considered which includes the full three-dimensional Euler equations. The initial interaction at an arbitrary curved surface is resolved in time by a convergent series. Among other features the solution exhibits shock, contact, and expansion waves as well as sound waves propagating on characteristic surfaces. The expansion waves correspond to he one-dimensional rarefactions but have a more complicated structure. The sound waves are generated in place of zero strength shocks, and they are caused by mismatches in derivatives.

Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves

NASA Astrophysics Data System (ADS)

Barker, Blake; Jung, Soyeun; Zumbrun, Kevin

2018-03-01

Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability in conservation laws and (ii) use these conditions to find families of periodic solutions bifurcating from uniform states, numerically continuing these families into the large-amplitude regime. For the examples studied, numerical stability analysis suggests that stable periodic waves can emerge either from supercritical Turing bifurcations or, via secondary bifurcation as amplitude is increased, from subcritical Turing bifurcations. This answers in the affirmative a question of Oh-Zumbrun whether stable periodic solutions of conservation laws can occur. Determination of a full small-amplitude stability diagram - specifically, determination of rigorous Eckhaus-type stability conditions - remains an interesting open problem.

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1982-01-01

Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.

CMS-Wave

DTIC Science & Technology

2015-10-30

Coastal Inlets Research Program CMS -Wave CMS -Wave is a two-dimensional spectral wind-wave generation and transformation model that employs a forward...marching, finite-difference method to solve the wave action conservation equation. Capabilities of CMS -Wave include wave shoaling, refraction... CMS -Wave can be used in either on a half- or full-plane mode, with primary waves propagating from the seaward boundary toward shore. It can

Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.

A Novel Blast-mitigation Concept for Light Tactical Vehicles

DTIC Science & Technology

2013-01-01

analysis which utilizes the mass and energy (but not linear momentum ) conservation equations is provided. It should be noted that the identical final...results could be obtained using an analogous analysis which combines the mass and the linear momentum conservation equations. For a calorically...governing mass, linear momentum and energy conservation and heat conduction equations are solved within ABAQUS/ Explicit with a second-order accurate

7 CFR 610.13 - Equations for predicting soil loss due to wind erosion.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 6 2014-01-01 2014-01-01 false Equations for predicting soil loss due to wind erosion... RESOURCES CONSERVATION SERVICE, DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.13 Equations for predicting soil loss due to wind erosion. (a) The...

7 CFR 610.13 - Equations for predicting soil loss due to wind erosion.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 6 2010-01-01 2010-01-01 false Equations for predicting soil loss due to wind erosion... RESOURCES CONSERVATION SERVICE, DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.13 Equations for predicting soil loss due to wind erosion. (a) The...

7 CFR 610.13 - Equations for predicting soil loss due to wind erosion.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 7 Agriculture 6 2012-01-01 2012-01-01 false Equations for predicting soil loss due to wind erosion... RESOURCES CONSERVATION SERVICE, DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.13 Equations for predicting soil loss due to wind erosion. (a) The...

7 CFR 610.13 - Equations for predicting soil loss due to wind erosion.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 7 Agriculture 6 2011-01-01 2011-01-01 false Equations for predicting soil loss due to wind erosion... RESOURCES CONSERVATION SERVICE, DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.13 Equations for predicting soil loss due to wind erosion. (a) The...

7 CFR 610.13 - Equations for predicting soil loss due to wind erosion.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 7 Agriculture 6 2013-01-01 2013-01-01 false Equations for predicting soil loss due to wind erosion... RESOURCES CONSERVATION SERVICE, DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.13 Equations for predicting soil loss due to wind erosion. (a) The...

On conservation laws for a generalized Boussinesq equation

NASA Astrophysics Data System (ADS)

Anco, S.; Rosa, M.; Gandarias, M. L.

2017-07-01

In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. By using the low order conservation laws we apply the conservation laws multiplier method to the associated potential systems.

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Simbanefayi, Innocent; Khalique, Chaudry Masood

2018-03-01

In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Variational symmetries, conserved quantities and identities for several equations of mathematical physics

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

Donchev, Veliko, E-mail: velikod@ie.bas.bg

2014-03-15

We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.

Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny-Lin equation

NASA Astrophysics Data System (ADS)

Rashidi, Saeede; Hejazi, S. Reza

This paper investigates the invariance properties of the time fractional Benny-Lin equation with Riemann-Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto-Sivashinsky equation and Navier-Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny-Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

Recent applications of the transonic wing analysis computer code, TWING

NASA Technical Reports Server (NTRS)

Subramanian, N. R.; Holst, T. L.; Thomas, S. D.

1982-01-01

An evaluation of the transonic-wing-analysis computer code TWING is given. TWING utilizes a fully implicit approximate factorization iteration scheme to solve the full potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations were analyzed, and the limits of applicability of this code was evaluated. Comparisons of computed results were made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative full potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

Hyperbolic conservation laws and numerical methods

NASA Technical Reports Server (NTRS)

Leveque, Randall J.

1990-01-01

The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.

Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg–de Vries equation

PubMed Central

Bridges, Thomas J.

2016-01-01

Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg–de Vries (KdV) equation. The coefficients in the emergent KdV equation have a geometrical interpretation in terms of projection of the vector components of the conservation law. The theory herein is restricted to two phases to simplify presentation, with extensions to any finite dimension discussed in the concluding remarks. Two applications of the theory are presented: a coupled nonlinear Schrödinger equation and two-layer shallow-water hydrodynamics with a free surface. Both have two-phase solutions where criticality and the properties of the emergent KdV equation can be determined analytically. PMID:28119546

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

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

Dumbser, Michael, E-mail: michael.dumbser@unitn.it; Balsara, Dinshaw S., E-mail: dbalsara@nd.edu

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearlymore » degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for. -- Highlights: •New simple and general path-conservative formulation of the HLLEM Riemann solver. •Application to general conservative and non-conservative hyperbolic systems. •Inclusion of sub-structure and resolution of intermediate characteristic fields. •Well-balanced for single- and two-layer shallow water equations and multi-phase flows. •Euler equations with real equation of state, MHD equations, nonlinear elasticity.« less

The combustion program at CTR

NASA Technical Reports Server (NTRS)

Poinsot, Thierry J.

1993-01-01

Understanding and modeling of turbulent combustion are key problems in the computation of numerous practical systems. Because of the lack of analytical theories in this field and of the difficulty of performing precise experiments, direct numerical simulation (DNS) appears to be one of the most attractive tools to use in addressing this problem. The general objective of DNS of reacting flows is to improve our knowledge of turbulent combustion but also to use this information for turbulent combustion models. For the foreseeable future, numerical simulation of the full three-dimensional governing partial differential equations with variable density and transport properties as well as complex chemistry will remain intractable; thus, various levels of simplification will remain necessary. On one hand, the requirement to simplify is not necessarily a handicap: numerical simulations allow the researcher a degree of control in isolating specific physical phenomena that is inaccessible in experiments. CTR has pursued an intensive research program in the field of DNS for turbulent reacting flows since 1987. DNS of reacting flows is quite different from DNS of non-reacting flows: without reaction, the equations to solve are clearly the five conservation equations of the Navier Stokes system for compressible situations (four for incompressible cases), and the limitation of the approach is the Reynolds number (or in other words the number of points in the computation). For reacting flows, the choice of the equations, the species (each species will require one additional conservation equation), the chemical scheme, and the configuration itself is more complex.

Cubication of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada

2009-01-01

A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

DOE PAGES

Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.; ...

2016-09-01

We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity terms. The spectral method can also be used to solve the Landau equation andmore » a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.« less

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

NASA Technical Reports Server (NTRS)

Woods, Claudia M.; Brewe, David E.

1988-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

NASA Technical Reports Server (NTRS)

Woods, C. M.; Brewe, D. E.

1989-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

The use of multigrid techniques in the solution of the Elrod algorithm for a dynamically loaded journal bearing. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Woods, Claudia M.

1988-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed, utilizing a multigrid iterative technique. The code is compared with a presently existing direct solution in terms of computational time and accuracy. The model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobssen-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via liquid striations. The mixed nature of the equations (elliptic in the full film zone and nonelliptic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

General Navier–Stokes-like momentum and mass-energy equations

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

Monreal, Jorge, E-mail: jmonreal@mail.usf.edu

2015-03-15

A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.

On a new class of completely integrable nonlinear wave equations. II. Multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.

1987-11-01

The multi-Hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed. Infinitely many conservation laws had earlier been obtained for these equations. Starting from a (primary) Hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi-Hamiltonian structure are obtained and it is shown that the second Hamiltonian operator can be constructed solely through a knowledge of the first Hamiltonian function. The recursion operator which first appears at the level of bi-Hamiltonian structure gives rise to an infinite sequence of conserved Hamiltonians. It is found that in general there exist two different infinite sequences of conserved quantities for these equations. The recursion relation defining higher Hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the (k+1)st Hamiltonian operator which depends on the kth Hamiltonian function. The infinite sequence of conserved Hamiltonians are common to all the higher Hamiltonian structures. The equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri-Hamiltonian structure with two distinct infinite sets of conserved quantities. The isothermal case of γ=1 is an exceptional one that requires separate treatment. This corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to Poisson's equation in nonlinear acoustics.

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1985-01-01

A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.

Geometry of Conservation Laws for a Class of Parabolic Partial Differential Equations

NASA Astrophysics Data System (ADS)

Clelland, Jeanne Nielsen

1996-08-01

I consider the problem of computing the space of conservation laws for a second-order, parabolic partial differential equation for one function of three independent variables. The PDE is formulated as an exterior differential system {cal I} on a 12 -manifold M, and its conservation laws are identified with the vector space of closed 3-forms in the infinite prolongation of {cal I} modulo the so -called "trivial" conservation laws. I use the tools of exterior differential systems and Cartan's method of equivalence to study the structure of the space of conservation laws. My main result is:. Theorem. Any conservation law for a second-order, parabolic PDE for one function of three independent variables can be represented by a closed 3-form in the differential ideal {cal I} on the original 12-manifold M. I show that if a nontrivial conservation law exists, then {cal I} has a deprolongation to an equivalent system {cal J} on a 7-manifold N, and any conservation law for {cal I} can be expressed as a closed 3-form on N which lies in {cal J}. Furthermore, any such system in the real analytic category is locally equivalent to a system generated by a (parabolic) equation of the formA(u _{xx}u_{yy}-u_sp {xy}{2}) + B_1u_{xx }+2B_2u_{xy} +B_3u_ {yy}+C=0crwhere A, B_{i}, C are functions of x, y, t, u, u_{x}, u _{y}, u_{t}. I compute the space of conservation laws for several examples, and I begin the process of analyzing the general case using Cartan's method of equivalence. I show that the non-linearizable equation u_{t} = {1over2}e ^{-u}(u_{xx}+u_ {yy})has an infinite-dimensional space of conservation laws. This stands in contrast to the two-variable case, for which Bryant and Griffiths showed that any equation whose space of conservation laws has dimension 4 or more is locally equivalent to a linear equation, i.e., is linearizable.

Magnetohydrodynamic motion of a two-fluid plasma

DOE PAGES

Burby, Joshua W.

2017-07-21

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Magnetohydrodynamic motion of a two-fluid plasma

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

Burby, Joshua W.

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

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

Anton, Luis; MartI, Jose M; Ibanez, Jose M

2010-05-01

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, andmore » can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.« less

Nonlocal conservation laws of the constant astigmatism equation

NASA Astrophysics Data System (ADS)

Hlaváč, Adam; Marvan, Michal

2017-03-01

For the constant astigmatism equation, we construct a system of nonlocal conservation laws (an abelian covering) closed under the reciprocal transformations. The corresponding potentials are functionally independent modulo a Wronskian type relation.

Numerical study of nonlinear full wave acoustic propagation

NASA Astrophysics Data System (ADS)

Velasco-Segura, Roberto; Rendon, Pablo L.

2013-11-01

With the aim of describing nonlinear acoustic phenomena, a form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A CLAWPACK based, 2D finite-volume method using Roe's linearization has been implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a HIFU system, both with satisfactory results. The code is written for parallel execution on a GPU and improves performance by a factor of over 50 when compared to the standard CLAWPACK Fortran code. This code can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from modest models of diagnostic and therapeutic HIFU, parametric acoustic arrays, to acoustic wave guides. A couple of examples will be presented showing shock formation and oblique interaction. DGAPA PAPIIT IN110411, PAEP UNAM 2013.

On the Conservation of Cross Helicity and Wave Action in Solar-wind Models with Non-WKB Alfvén Wave Reflection

NASA Astrophysics Data System (ADS)

Chandran, Benjamin D. G.; Perez, Jean C.; Verscharen, Daniel; Klein, Kristopher G.; Mallet, Alfred

2015-09-01

The interaction between Alfvén-wave turbulence and the background solar wind affects the cross helicity (\\int {d}3x {\\boldsymbol{v}}\\cdot {\\boldsymbol{B}}) in two ways. Non-WKB reflection converts outward-propagating Alfvén waves into inward-propagating Alfvén waves and vice versa, and the turbulence transfers momentum to the background flow. When both effects are accounted for, the total cross helicity is conserved. In the special case that the background density and flow speed are independent of time, the equations of cross-helicity conservation and total-energy conservation can be combined to recover a well-known equation derived by Heinemann and Olbert that has been interpreted as a non-WKB generalization of wave-action conservation. This latter equation (in contrast to cross-helicity and energy conservation) does not hold when the background varies in time.

A comparative study of the nonuniqueness problem of the potential equation

NASA Technical Reports Server (NTRS)

Salas, M. D.; Jameson, A.; Melnik, R. E.

1985-01-01

The nonuniqueness problem occurring at transonic speeds with the conservative potential equation is investigated numerically. The study indicates that the problem is not an inviscid phenomenon, but results from approximate treatment of shock waves inherent in the conservative potential model. A new bound on the limit of validity of the conservative potential model is proposed.

Braneworld gravity within non-conservative gravitational theory

NASA Astrophysics Data System (ADS)

Fabris, J. C.; Caramês, Thiago R. P.; da Silva, J. M. Hoff

2018-05-01

We investigate the braneworld gravity starting from the non-conservative gravitational field equations in a five-dimensional bulk. The approach is based on the Gauss-Codazzi formalism along with the study of the braneworld consistency conditions. The effective gravitational equations on the brane are obtained and the constraint leading to a brane energy-momentum conservation is analyzed.

A semi-Lagrangian approach to the shallow water equation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Mccormick, Stephen F.; Ruge, John; Sholl, David S.; Yavneh, Irad

1993-01-01

We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.

Relativistic analogue of the Newtonian fluid energy equation with nucleosynthesis

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

Cardall, Christian Y.

In Newtonian fluid dynamics simulations in which composition has been tracked by a nuclear reaction network, energy generation due to composition changes has generally been handled as a separate source term in the energy equation. Here, a relativistic equation in conservative form for total fluid energy, obtained from the spacetime divergence of the stress-energy tensor, in principle encompasses such energy generation; but it is not explicitly manifest. An alternative relativistic energy equation in conservative form—in which the nuclear energy generation appears explicitly, and that reduces directly to the Newtonian internal+kinetic energy in the appropriate limit—emerges naturally and self-consistently from themore » difference of the equation for total fluid energy and the equation for baryon number conservation multiplied by the average baryon mass m, when m is expressed in terms of contributions from the nuclear species in the fluid, and allowed to be mutable.« less

Relativistic analogue of the Newtonian fluid energy equation with nucleosynthesis

DOE PAGES

Cardall, Christian Y.

2017-12-15

In Newtonian fluid dynamics simulations in which composition has been tracked by a nuclear reaction network, energy generation due to composition changes has generally been handled as a separate source term in the energy equation. Here, a relativistic equation in conservative form for total fluid energy, obtained from the spacetime divergence of the stress-energy tensor, in principle encompasses such energy generation; but it is not explicitly manifest. An alternative relativistic energy equation in conservative form—in which the nuclear energy generation appears explicitly, and that reduces directly to the Newtonian internal+kinetic energy in the appropriate limit—emerges naturally and self-consistently from themore » difference of the equation for total fluid energy and the equation for baryon number conservation multiplied by the average baryon mass m, when m is expressed in terms of contributions from the nuclear species in the fluid, and allowed to be mutable.« less

Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations.

PubMed

Bell, John B; Garcia, Alejandro L; Williams, Sarah A

2007-07-01

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

Full potential methods for analysis/design of complex aerospace configurations

NASA Technical Reports Server (NTRS)

Shankar, Vijaya; Szema, Kuo-Yen; Bonner, Ellwood

1986-01-01

The steady form of the full potential equation, in conservative form, is employed to analyze and design a wide variety of complex aerodynamic shapes. The nonlinear method is based on the theory of characteristic signal propagation coupled with novel flux biasing concepts and body-fitted mapping procedures. The resulting codes are vectorized for the CRAY XMP and the VPS-32 supercomputers. Use of the full potential nonlinear theory is demonstrated for a single-point supersonic wing design and a multipoint design for transonic maneuver/supersonic cruise/maneuver conditions. Achievement of high aerodynamic efficiency through numerical design is verified by wind tunnel tests. Other studies reported include analyses of a canard/wing/nacelle fighter geometry.

Conservational PDF Equations of Turbulence

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2010-01-01

Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Bart, Timothy J.; Kutler, Paul (Technical Monitor)

1998-01-01

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

Electromagnetic momentum and the energy–momentum tensor in a linear medium with magnetic and dielectric properties

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

Crenshaw, Michael E., E-mail: michael.e.crenshaw4.civ@mail.mil

2014-04-15

In a continuum setting, the energy–momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy–momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derivemore » electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material four-divergence of the traceless, symmetric total energy–momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the Abraham–Minkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy–momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.« less

Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics

NASA Astrophysics Data System (ADS)

Webb, G. M.; Anco, S. C.

2016-02-01

The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.

Consistent description of kinetic equation with triangle anomaly

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

Pu Shi; Gao Jianhua; Wang Qun

2011-05-01

We provide a consistent description of the kinetic equation with a triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for the minimum number of unknown coefficients in onemore » charge and two charge cases by solving the constraining equations.« less

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

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

Ghosh, Debojyoti; Constantinescu, Emil M.

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essentialmore » because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature.« less

Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions

NASA Astrophysics Data System (ADS)

El, G. A.; Kamchatnov, A. M.; Pavlov, M. V.; Zykov, S. A.

2011-04-01

We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between solitons. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N-component `cold-gas' hydrodynamic reductions. We prove that these reductions represent integrable linearly degenerate hydrodynamic type systems for arbitrary N which is a strong evidence in favour of integrability of the full kinetic equation. We derive compact explicit representations for the Riemann invariants and characteristic velocities of the hydrodynamic reductions in terms of the `cold-gas' component densities and construct a number of exact solutions having special properties (quasiperiodic, self-similar). Hydrodynamic symmetries are then derived and investigated. The obtained results shed light on the structure of a continuum limit for a large class of integrable systems of hydrodynamic type and are also relevant to the description of turbulent motion in conservative compressible flows.

Numerical simulation of steady and unsteady asymmetric vortical flow

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Wong, Tin-Chee; Liu, C. H.

1992-01-01

The unsteady, compressible, thin-layer, Navier-Stokes (NS) equations are solved to simulate steady and unsteady, asymmetric, vortical laminar flow around cones at high incidences and supersonic Mach numbers. The equations are solved by using an implicit, upwind, flux-difference splitting (FDS), finite-volume scheme. The locally conical flow assumption is used and the solutions are obtained by forcing the conserved components of the flowfield vector to be equal at two axial stations located at 0.95 and 1.0. Computational examples cover steady and unsteady asymmetric flows around a circular cone and its control using side strakes. The unsteady asymmetric flow solution around the circular cone has also been validated using the upwind, flux-vector splitting (FVS) scheme with the thin-layer NS equations and the upwind FDS with the full NS equations. The results are in excellent agreement with each other. Unsteady asymmetric flows are also presented for elliptic- and diamond-section cones, which model asymmetric vortex shedding around round- and sharp-edged delta winds.

A conservative, relativistic Fokker-Planck solver for runaway electrons

NASA Astrophysics Data System (ADS)

Chacon, Luis; Taitano, W.; Tang, X.; Guo, Z.; McDevitt, C.

2017-10-01

Relativistic runaway electrons develop when electric fields surpass a critical electric field, Ec =EDvth/c 2 , with ED the Dreicer field (which is the electric field at which the whole thermal electron population runs away). Above this critical field, electron tails accelerate relativistically until they are arrested by radiative processes. In regimes above this critical electric field (but below the Dreicer field), correctly capturing the interplay between the electron thermal population and the runaway tail is key, and demands a full nonlinear relativistic Fokker-Planck treatment. In this presentation, we report on progress towards a fully conservative, implicit, adaptive implementation of the relativistic electron Fokker-Planck equation. Strict conservation properties, as well as positivity preservation, are a must to avoid spurious numerical effects, and to be able to capture tenuous electron runaway tails for fields just above Ec.

The fundamental equation of eddy covariance and its application in flux measurements

Treesearch

Lianhong Gu; William J. Massman; Ray Leuning; Stephen G. Pallardy; Tilden Meyers; Paul J. Hanson; Jeffery S. Riggs; Kevin P. Hosman; Bai Yang

2012-01-01

A fundamental equation of eddy covariance (FQEC) is derived that allows the net ecosystem exchange (NEE) Ns of a specified atmospheric constituent s to be measured with the constraint of conservation of any other atmospheric constituent (e.g. N2, argon, or dry air). It is shown that if the condition [equation, see PDF] is true, the conservation of mass can be applied...

LETTER TO THE EDITOR: Bicomplexes and conservation laws in non-Abelian Toda models

NASA Astrophysics Data System (ADS)

Gueuvoghlanian, E. P.

2001-08-01

A bicomplex structure is associated with the Leznov-Saveliev equation of integrable models. The linear problem associated with the zero-curvature condition is derived in terms of the bicomplex linear equation. The explicit example of a non-Abelian conformal affine Toda model is discussed in detail and its conservation laws are derived from the zero-curvature representation of its equation of motion.

Fradkin-Bacry-Ruegg-Souriau perihelion vector for Gorringe-Leach equations

NASA Astrophysics Data System (ADS)

Grandati, Yves; Bérard, Alain; Mohrbach, Hervé

2010-02-01

We show that every generalized Gorringe-Leach equation admits an associated Fradkin-Bacry-Ruegg-Souriau’s vector which, in general, is only a piecewise conserved quantity. In the case of dualizable generalized Gorringe-Leach equations, which include the case of conservative motions in central power law potentials, the image sets of the FBRS vectors for dual classes are dual images of each other.

International Conference on Hyperbolic Problems (2nd). Theory, Numerical Methods and Applications, 14-18 March 1988

DTIC Science & Technology

1988-01-01

of this abstract got a spontaneous development of a transverse wave-strucure in a shock-oriented coordinate system without per- turbing the global ...We develop a formal asymptotic theory for hyperbolic conservation laws with large amplitude, rapidly varying initial data [1]. For small times, the...HUnefelderstr. 1-S, D-2800 Bremen 1 Today the most accurate and cost effective industrial codes used for aircraft design are based on full potential equations

Three-dimensional simulation of vortex breakdown

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Salas, M. D.

1990-01-01

The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state.

TAIR: A transonic airfoil analysis computer code

NASA Technical Reports Server (NTRS)

Dougherty, F. C.; Holst, T. L.; Grundy, K. L.; Thomas, S. D.

1981-01-01

The operation of the TAIR (Transonic AIRfoil) computer code, which uses a fast, fully implicit algorithm to solve the conservative full-potential equation for transonic flow fields about arbitrary airfoils, is described on two levels of sophistication: simplified operation and detailed operation. The program organization and theory are elaborated to simplify modification of TAIR for new applications. Examples with input and output are given for a wide range of cases, including incompressible, subcritical compressible, and transonic calculations.

BMS3 invariant fluid dynamics at null infinity

NASA Astrophysics Data System (ADS)

Penna, Robert F.

2018-02-01

We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary’s equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie–Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden–Ratiu–Weinstein formulation of the compressible Euler equations on a manifold, M, as Hamiltonian flow on the dual of the Lie algebra of \

Path length differencing and energy conservation of the S[sub N] Boltzmann/Spencer-Lewis equation

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

Filippone, W.L.; Monahan, S.P.

It is shown that the S[sub N] Boltzmann/Spencer-Lewis equations conserve energy locally if and only if they satisfy particle balance and diamond differencing is used in path length. In contrast, the spatial differencing schemes have no bearing on the energy balance. Energy is conserved globally if it is conserved locally and the multigroup cross sections are energy conserving. Although the coupled electron-photon cross sections generated by CEPXS conserve particles and charge, they do not precisely conserve energy. It is demonstrated that these cross sections can be adjusted such that particles, charge, and energy are conserved. Finally, since a conventional negativemore » flux fixup destroys energy balance when applied to path legend, a modified fixup scheme that does not is presented.« less

On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations

NASA Technical Reports Server (NTRS)

Deshpande, S. M.

1986-01-01

The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions.

Hamiltonian structures for systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Olver, Peter J.; Nutku, Yavuz

1988-07-01

The bi-Hamiltonian structure for a large class of one-dimensional hyberbolic systems of conservation laws in two field variables, including the equations of gas dynamics, shallow water waves, one-dimensional elastic media, and the Born-Infeld equation from nonlinear electrodynamics, is exhibited. For polytropic gas dynamics, these results lead to a quadri-Hamiltonian structure. New higher-order entropy-flux pairs (conservation laws) and higher-order symmetries are exhibited.

Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Zhang, Xiang-Zhi; Dong, Huan-He

2017-12-01

Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and (1+1)-dimensional and (2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally, we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the (1+1) and (2+1)-dimensional Toda-type equations. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

Higher-order jump conditions for conservation laws

NASA Astrophysics Data System (ADS)

Oksuzoglu, Hakan

2018-04-01

The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynamics is the Rankine-Hugoniot conditions for the shock speed. Here, we provide an expression for the acceleration of the discontinuity in terms of the state variables and their spatial derivatives on both sides. We derive a jump condition for the shock acceleration. Using this general expression, we show how to obtain explicit shock acceleration formulas for nonlinear hyperbolic conservation laws. We start with the Burgers' equation and check the derived formula with an analytical solution. We next derive formulas for the Shallow Water Equations and the Euler Equations of Gas Dynamics. We will verify our formulas for the Euler Equations using an exact solution for the spherically symmetric blast wave problem. In addition, we discuss the potential use of these formulas for the implementation of shock fitting methods.

How to Obtain the Covariant Form of Maxwell's Equations from the Continuity Equation

ERIC Educational Resources Information Center

Heras, Jose A.

2009-01-01

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

Similarity considerations and conservation laws for magneto-static atmospheres

NASA Technical Reports Server (NTRS)

Webb, G. M.

1986-01-01

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.

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.

Numerical Simulation of Combustion and Rotor-Stator Interaction in a Turbine Combustor

DOE PAGES

Isvoranu, Dragos D.; Cizmas, Paul G. A.

2003-01-01

This article presents the development of a numerical algorithm for the computation of flow and combustion in a turbine combustor. The flow and combustion are modeled by the Reynolds-averaged Navier-Stokes equations coupled with the species-conservation equations. The chemistry model used herein is a two-step, global, finite-rate combustion model for methane and combustion gases. The governing equations are written in the strong conservation form and solved using a fully implicit, finite-difference approximation. The gas dynamics and chemistry equations are fully decoupled. A correction technique has been developed to enforce the conservation of mass fractions. The numerical algorithm developed herein has beenmore » used to investigate the flow and combustion in a one-stage turbine combustor.« less

AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

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

Zhao Dun; Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000; Zhang Yujuan

2011-04-15

By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLSmore » systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.« less

Mass conservation: 1-D open channel flow equations

USGS Publications Warehouse

DeLong, Lewis L.

1989-01-01

Unsteady flow simulation in natural rivers is often complicated by meandering channels of compound section. Hydraulic properties and the length of the wetted channel may vary significantly as a meandering river inundates its adjacent floodplain. The one-dimensional, unsteady, open-channel flow equations can be extended to simulate floods in channels of compound section. It will be shown that equations derived from the addition of differential equations individually describing flow in main and overbank channels do not in general conserve mass when overbank and main channels are of different lengths.

Uniqueness of Mass-Conserving Self-similar Solutions to Smoluchowski's Coagulation Equation with Inverse Power Law Kernels

NASA Astrophysics Data System (ADS)

Laurençot, Philippe

2018-03-01

Uniqueness of mass-conserving self-similar solutions to Smoluchowski's coagulation equation is shown when the coagulation kernel K is given by K(x,x_*)=2(x x_*)^{-α } , (x,x_*)\\in (0,∞)^2 , for some α >0.

Discrete conservation properties for shallow water flows using mixed mimetic spectral elements

NASA Astrophysics Data System (ADS)

Lee, D.; Palha, A.; Gerritsma, M.

2018-03-01

A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in one dimension. These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as higher moments (energy, potential enstrophy), subject to the truncation error of the time stepping scheme. The continuity equation is solved in the strong form, such that mass conservation holds point wise, while the momentum equation is solved in the weak form such that vorticity is globally conserved. While mass, vorticity and energy conservation hold for any quadrature rule, potential enstrophy conservation is dependent on exact spatial integration. The method possesses a weak form statement of geostrophic balance due to the compatible nature of the solution spaces and arbitrarily high order spatial error convergence.

Generalized Maxwell equations and charge conservation censorship

NASA Astrophysics Data System (ADS)

Modanese, G.

2017-02-01

The Aharonov-Bohm electrodynamics is a generalization of Maxwell theory with reduced gauge invariance. It allows to couple the electromagnetic field to a charge which is not locally conserved, and has an additional degree of freedom, the scalar field S = ∂αAα, usually interpreted as a longitudinal wave component. By reformulating the theory in a compact Lagrangian formalism, we are able to eliminate S explicitly from the dynamics and we obtain generalized Maxwell equation with interesting properties: they give ∂μFμν as the (conserved) sum of the (possibly non-conserved) physical current density jν, and a “secondary” current density iν which is a nonlocal function of jν. This implies that any non-conservation of jν is effectively “censored” by the observable field Fμν, and yet it may have real physical consequences. We give examples of stationary solutions which display these properties. Possible applications are to systems where local charge conservation is violated due to anomalies of the Adler-Bell-Jackiw (ABJ) kind or to macroscopic quantum tunnelling with currents which do not satisfy a local continuity equation.

Axisymmetric charge-conservative electromagnetic particle simulation algorithm on unstructured grids: Application to microwave vacuum electronic devices

NASA Astrophysics Data System (ADS)

Na, Dong-Yeop; Omelchenko, Yuri A.; Moon, Haksu; Borges, Ben-Hur V.; Teixeira, Fernando L.

2017-10-01

We present a charge-conservative electromagnetic particle-in-cell (EM-PIC) algorithm optimized for the analysis of vacuum electronic devices (VEDs) with cylindrical symmetry (axisymmetry). We exploit the axisymmetry present in the device geometry, fields, and sources to reduce the dimensionality of the problem from 3D to 2D. Further, we employ 'transformation optics' principles to map the original problem in polar coordinates with metric tensor diag (1 ,ρ2 , 1) to an equivalent problem on a Cartesian metric tensor diag (1 , 1 , 1) with an effective (artificial) inhomogeneous medium introduced. The resulting problem in the meridian (ρz) plane is discretized using an unstructured 2D mesh considering TEϕ-polarized fields. Electromagnetic field and source (node-based charges and edge-based currents) variables are expressed as differential forms of various degrees, and discretized using Whitney forms. Using leapfrog time integration, we obtain a mixed E - B finite-element time-domain scheme for the full-discrete Maxwell's equations. We achieve a local and explicit time update for the field equations by employing the sparse approximate inverse (SPAI) algorithm. Interpolating field values to particles' positions for solving Newton-Lorentz equations of motion is also done via Whitney forms. Particles are advanced using the Boris algorithm with relativistic correction. A recently introduced charge-conserving scatter scheme tailored for 2D unstructured grids is used in the scatter step. The algorithm is validated considering cylindrical cavity and space-charge-limited cylindrical diode problems. We use the algorithm to investigate the physical performance of VEDs designed to harness particle bunching effects arising from the coherent (resonance) Cerenkov electron beam interactions within micro-machined slow wave structures.

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

2014-09-01

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

A minimum entropy principle in the gas dynamics equations

NASA Technical Reports Server (NTRS)

Tadmor, E.

1986-01-01

Let u(x bar,t) be a weak solution of the Euler equations, governing the inviscid polytropic gas dynamics; in addition, u(x bar, t) is assumed to respect the usual entropy conditions connected with the conservative Euler equations. We show that such entropy solutions of the gas dynamics equations satisfy a minimum entropy principle, namely, that the spatial minimum of their specific entropy, (Ess inf s(u(x,t)))/x, is an increasing function of time. This principle equally applies to discrete approximations of the Euler equations such as the Godunov-type and Lax-Friedrichs schemes. Our derivation of this minimum principle makes use of the fact that there is a family of generalized entrophy functions connected with the conservative Euler equations.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations

NASA Astrophysics Data System (ADS)

Zlotnik, A. A.

2017-04-01

The multidimensional quasi-gasdynamic system written in the form of mass, momentum, and total energy balance equations for a perfect polytropic gas with allowance for a body force and a heat source is considered. A new conservative symmetric spatial discretization of these equations on a nonuniform rectangular grid is constructed (with the basic unknown functions—density, velocity, and temperature—defined on a common grid and with fluxes and viscous stresses defined on staggered grids). Primary attention is given to the analysis of entropy behavior: the discretization is specially constructed so that the total entropy does not decrease. This is achieved via a substantial revision of the standard discretization and applying numerous original features. A simplification of the constructed discretization serves as a conservative discretization with nondecreasing total entropy for the simpler quasi-hydrodynamic system of equations. In the absence of regularizing terms, the results also hold for the Navier-Stokes equations of a viscous compressible heat-conducting gas.

A kinetic equation with kinetic entropy functions for scalar conservation laws

NASA Technical Reports Server (NTRS)

Perthame, Benoit; Tadmor, Eitan

1990-01-01

A nonlinear kinetic equation is constructed and proved to be well-adapted to describe general multidimensional scalar conservation laws. In particular, it is proved to be well-posed uniformly in epsilon - the microscopic scale. It is also shown that the proposed kinetic equation is equipped with a family of kinetic entropy functions - analogous to Boltzmann's microscopic H-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, it is proved by both - BV compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with epsilon below 0 to the unique entropy solution of the corresponding conservation law.

Scale-Invariant Forms of Conservation Equations in Reactive Fields and a Modified Hydro-Thermo-Diffusive Theory of Laminar Flames

NASA Technical Reports Server (NTRS)

Sohrab, Siavash H.; Piltch, Nancy (Technical Monitor)

2000-01-01

A scale-invariant model of statistical mechanics is applied to present invariant forms of mass, energy, linear, and angular momentum conservation equations in reactive fields. The resulting conservation equations at molecular-dynamic scale are solved by the method of large activation energy asymptotics to describe the hydro-thermo-diffusive structure of laminar premixed flames. The predicted temperature and velocity profiles are in agreement with the observations. Also, with realistic physico-chemical properties and chemical-kinetic parameters for a single-step overall combustion of stoichiometric methane-air premixed flame, the laminar flame propagation velocity of 42.1 cm/s is calculated in agreement with the experimental value.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

NASA Astrophysics Data System (ADS)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

Generalized continuity equations from two-field Schrödinger Lagrangians

NASA Astrophysics Data System (ADS)

Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.

2016-11-01

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.

Students' Understanding of Conservation of Matter, Stoichiometry and Balancing Equations in Indonesia

ERIC Educational Resources Information Center

Agung, Salamah; Schwartz, Marc S.

2007-01-01

This study examines Indonesian students' understanding of conservation of matter, balancing of equations and stoichiometry. Eight hundred and sixty-seven Grade 12 students from 22 schools across four different cities in two developed provinces in Indonesia participated in the study. Nineteen teachers also participated in order to validate the…

Spin-Orbit Coupling and the Conservation of Angular Momentum

ERIC Educational Resources Information Center

Hnizdo, V.

2012-01-01

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the…

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

An energy and potential enstrophy conserving scheme for the shallow water equations. [orography effects on atmospheric circulation

NASA Technical Reports Server (NTRS)

Arakawa, A.; Lamb, V. R.

1979-01-01

A three-dimensional finite difference scheme for the solution of the shallow water momentum equations which accounts for the conservation of potential enstrophy in the flow of a homogeneous incompressible shallow atmosphere over steep topography as well as for total energy conservation is presented. The scheme is derived to be consistent with a reasonable scheme for potential vorticity advection in a long-term integration for a general flow with divergent mass flux. Numerical comparisons of the characteristics of the present potential enstrophy-conserving scheme with those of a scheme that conserves potential enstrophy only for purely horizontal nondivergent flow are presented which demonstrate the reduction of computational noise in the wind field with the enstrophy-conserving scheme and its convergence even in relatively coarse grids.

Second- and third-order upwind difference schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Yang, J. Y.

1984-01-01

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1993-01-01

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1994-01-01

The primary accomplishments of the project are as follows: (1) Using the transonic small perturbation equation as a flowfield model, the project demonstrated that the quasi-analytical method could be used to obtain aerodynamic sensitivity coefficients for airfoils at subsonic, transonic, and supersonic conditions for design variables such as Mach number, airfoil thickness, maximum camber, angle of attack, and location of maximum camber. It was established that the quasi-analytical approach was an accurate method for obtaining aerodynamic sensitivity derivatives for airfoils at transonic conditions and usually more efficient than the finite difference approach. (2) The usage of symbolic manipulation software to determine the appropriate expressions and computer coding associated with the quasi-analytical method for sensitivity derivatives was investigated. Using the three dimensional fully conservative full potential flowfield model, it was determined that symbolic manipulation along with a chain rule approach was extremely useful in developing a combined flowfield and quasi-analytical sensitivity derivative code capable of considering a large number of realistic design variables. (3) Using the three dimensional fully conservative full potential flowfield model, the quasi-analytical method was applied to swept wings (i.e. three dimensional) at transonic flow conditions. (4) The incremental iterative technique has been applied to the three dimensional transonic nonlinear small perturbation flowfield formulation, an equivalent plate deflection model, and the associated aerodynamic and structural discipline sensitivity equations; and coupled aeroelastic results for an aspect ratio three wing in transonic flow have been obtained.

From Feynman rules to conserved quantum numbers, I

NASA Astrophysics Data System (ADS)

Nogueira, P.

2017-05-01

In the context of Quantum Field Theory (QFT) there is often the need to find sets of graph-like diagrams (the so-called Feynman diagrams) for a given physical model. If negative, the answer to the related problem 'Are there any diagrams with this set of external fields?' may settle certain physical questions at once. Here the latter problem is formulated in terms of a system of linear diophantine equations derived from the Lagrangian density, from which necessary conditions for the existence of the required diagrams may be obtained. Those conditions are equalities that look like either linear diophantine equations or linear modular (i.e. congruence) equations, and may be found by means of fairly simple algorithms that involve integer computations. The diophantine equations so obtained represent (particle) number conservation rules, and are related to the conserved (additive) quantum numbers that may be assigned to the fields of the model.

Ion-Conserving Modified Poisson-Boltzmann Theory Considering a Steric Effect in an Electrolyte

NASA Astrophysics Data System (ADS)

Sugioka, Hideyuki

2016-12-01

The modified Poisson-Nernst-Planck (MPNP) and modified Poisson-Boltzmann (MPB) equations are well known as fundamental equations that consider a steric effect, which prevents unphysical ion concentrations. However, it is unclear whether they are equivalent or not. To clarify this problem, we propose an improved free energy formulation that considers a steric limit with an ion-conserving condition and successfully derive the ion-conserving modified Poisson-Boltzmann (IC-MPB) equations that are equivalent to the MPNP equations. Furthermore, we numerically examine the equivalence by comparing between the IC-MPB solutions obtained by the Newton method and the steady MPNP solutions obtained by the finite-element finite-volume method. A surprising aspect of our finding is that the MPB solutions are much different from the MPNP (IC-MPB) solutions in a confined space. We consider that our findings will significantly contribute to understanding the surface science between solids and liquids.

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Cole, Helen; Chen, C. P.

2005-01-01

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

Governing equations for electro-conjugate fluid flow

NASA Astrophysics Data System (ADS)

Hosoda, K.; Takemura, K.; Fukagata, K.; Yokota, S.; Edamura, K.

2013-12-01

An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

Dissipation-preserving spectral element method for damped seismic wave equations

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai; Wang, Yushun

2017-12-01

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

NASA Technical Reports Server (NTRS)

Scott, R. K.

1972-01-01

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets

DOE PAGES

Jibben, Zechariah Joel; Herrmann, Marcus

2017-08-24

Here, we present a Runge-Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constantmore » with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.« less

A (2+1)-dimensional Korteweg-de Vries type equation in water waves: Lie symmetry analysis; multiple exp-function method; conservation laws

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid

2016-05-01

We consider a (2+1)-dimensional Korteweg-de Vries type equation which models the shallow-water waves, surface and internal waves. In the analysis, we use the Lie symmetry method and the multiple exp-function method. Furthermore, conservation laws are computed using the multiplier method.

The P1-RKDG method for two-dimensional Euler equations of gas dynamics

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1991-01-01

A class of nonlinearly stable Runge-Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws is investigated. Two dimensional Euler equations for gas dynamics are solved using P1 elements. The generalization of the local projections, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions is discussed. Numerical examples include the standard regular shock reflection problem, the forward facing step problem, and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of the approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods.

Evading the non-continuity equation in the f( R, T) cosmology

NASA Astrophysics Data System (ADS)

Moraes, P. H. R. S.; Correa, R. A. C.; Ribeiro, G.

2018-03-01

We present a new approach for the f( R, T) gravity formalism, by thoroughly exploring the extra terms of its effective energy-momentum tensor T_{μ ν }^eff, which we name \\tilde{T}_{μ ν }, so that T_{μ ν }^eff=T_{μ ν }+\\tilde{T}_{μ ν }, with T_{μ ν } being the usual energy-momentum tensor of matter. Purely from the Bianchi identities, we obtain the conservation of both parts of the effective energy-momentum tensor, rather than the non-conservation of T_{μ ν }, originally occurring in the f( R, T) theories. In this way, the intriguing scenario of matter creation, which still lacks observational evidence, is evaded. One is left, then, with two sets of cosmological equations to be solved: the Friedmann-like equations along with the conservation of T_{μ ν } and along with the conservation of \\tilde{T}_{μ ν }. We present a physical interpretation for the conservation of \\tilde{T}_{μ ν }, which can be related to the presence of stiff matter in the universe. The cosmological consequences of this approach are presented and discussed as well as the benefits of evading the matter energy-momentum tensor non-conservation.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

NASA Astrophysics Data System (ADS)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

A Reduced-Order Model for Efficient Simulation of Synthetic Jet Actuators

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2003-01-01

A new reduced-order model of multidimensional synthetic jet actuators that combines the accuracy and conservation properties of full numerical simulation methods with the efficiency of simplified zero-order models is proposed. The multidimensional actuator is simulated by solving the time-dependent compressible quasi-1-D Euler equations, while the diaphragm is modeled as a moving boundary. The governing equations are approximated with a fourth-order finite difference scheme on a moving mesh such that one of the mesh boundaries coincides with the diaphragm. The reduced-order model of the actuator has several advantages. In contrast to the 3-D models, this approach provides conservation of mass, momentum, and energy. Furthermore, the new method is computationally much more efficient than the multidimensional Navier-Stokes simulation of the actuator cavity flow, while providing practically the same accuracy in the exterior flowfield. The most distinctive feature of the present model is its ability to predict the resonance characteristics of synthetic jet actuators; this is not practical when using the 3-D models because of the computational cost involved. Numerical results demonstrating the accuracy of the new reduced-order model and its limitations are presented.

Comparison of Fully-Compressible Equation Sets for Atmospheric Dynamics

NASA Technical Reports Server (NTRS)

Ahmad, Nashat N.

2016-01-01

Traditionally, the equation for the conservation of energy used in atmospheric models is based on potential temperature and is used in place of the total energy conservation. This paper compares the application of the two equations sets for both the Euler and the Navier-Stokes solutions using several benchmark test cases. A high-resolution wave-propagation method which accurately takes into account the source term due to gravity is used for computing the non-hydrostatic atmospheric flows. It is demonstrated that there is little to no difference between the results obtained using the two different equation sets for Euler as well as Navier-Stokes solutions.

Relations for estimating unit-hydrograph parameters in New Mexico

USGS Publications Warehouse

Waltemeyer, Scott D.

2001-01-01

Data collected from 20 U.S. Geological Survey streamflow-gaging stations, most of which were operated in New Mexico between about 1969 and 1977, were used to define hydrograph characteristics for small New Mexico streams. Drainage areas for the gaging stations ranged from 0.23 to 18.2 square miles. Observed values for the hydrograph characteristics were determined for 87 of the most significant rainfall-runoff events at these gaging stations and were used to define regional regression relations with basin characteristics. Regional relations defined lag time (tl), time of concentration (tc), and time to peak (tp) as functions of stream length and basin shape. The regional equation developed for time of concentration for New Mexico agrees well with the Kirpich equation developed for Tennessee. The Kirpich equation is based on stream length and channel slope, whereas the New Mexico equation is based on stream length and basin shape. Both equations, however, underestimate tc when applied to larger basins where tc is greater than about 2 hours. The median ratio between tp and tc for the observed data was 0.66, which equals the value (0.67) recommended by the Natural Resources Conservation Service (formerly the Soil Conservation Service). However, the median ratio between tl and tc was only 0.42, whereas the commonly used ratio is 0.60. A relation also was developed between unit-peak discharge (qu) and time of concentration. The unit-peak discharge relation is similar in slope to the Natural Resources Conservation Service equation, but the equation developed for New Mexico in this study produces estimates of qu that range from two to three times as large as those estimated from the Natural Resources Conservation Service equation. An average value of 833 was determined for the empirical constant Kp. A default value of 484 has been used by the Natural Resources Conservation Service when site-specific data are not available. The use of a lower value of Kp in calculations generally results in a lower peak discharge. A relation between the empirical constant Kp and average channel slope was defined in this study. The predicted Kp values from the equation ranged from 530 to 964 for the 20 flood-hydrograph gaging stations. The standard error of estimate for the equation is 36 percent.

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

NASA Astrophysics Data System (ADS)

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-01

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

On buffer layers as non-reflecting computational boundaries

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Turkel, Eli L.

1996-01-01

We examine an absorbing buffer layer technique for use as a non-reflecting boundary condition in the numerical simulation of flows. One such formulation was by Ta'asan and Nark for the linearized Euler equations. They modified the flow inside the buffer zone to artificially make it supersonic in the layer. We examine how this approach can be extended to the nonlinear Euler equations. We consider both a conservative and a non-conservative form modifying the governing equations in the buffer layer. We compare this with the case that the governing equations in the layer are the same as in the interior domain. We test the effectiveness of these buffer layers by a simulation of an excited axisymmetric jet based on a nonlinear compressible Navier-Stokes equations.

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field.

PubMed

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-28

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

Conservative DEC Discretization of Incompressible Navier-Stokes Equations on Arbitrary Surface Simplicial Meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh; Hirani, Anil; Samtaney, Ravi

2017-11-01

A conservative discretization of incompressible Navier-Stokes equations over surfaces is developed using discrete exterior calculus (DEC). The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of signed diagonal Hodge star operators, while using the circumcentric dual defined on arbitrary meshes, is shown to produce correct solutions even when many non-Delaunay triangles pairs exist. This allows the DEC discretization to admit arbitrary surface simplicial meshes, in contrast to the previously held notion that DEC was limited only to Delaunay meshes. The discretization scheme is presented along with several numerical test cases demonstrating its numerical convergence and conservation properties. Recent developments regarding the extension to conservative higher order methods are also presented. KAUST Baseline Research Funds of R. Samtaney.

Two-level schemes for the advection equation

NASA Astrophysics Data System (ADS)

Vabishchevich, Petr N.

2018-06-01

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

Two-Layer Viscous Shallow-Water Equations and Conservation Laws

NASA Astrophysics Data System (ADS)

Kanayama, Hiroshi; Dan, Hiroshi

In our previous papers, the two-layer viscous shallow-water equations were derived from the three-dimensional Navier-Stokes equations under the hydrostatic assumption. Also, it was noted that the combination of upper and lower equations in the two-layer model produces the classical one-layer equations if the density of each layer is the same. Then, the two-layer equations were approximated by a finite element method which followed our numerical scheme established for the one-layer model in 1978. Also, it was numerically demonstrated that the interfacial instability generated when the densities are the same can be eliminated by providing a sufficient density difference. In this paper, we newly show that conservation laws are still valid in the two-layer model. Also, we show results of a new physical experiment for the interfacial instability.

A discrete model on Sierpinski gasket substrate for a conserved current equation with a conservative noise

NASA Astrophysics Data System (ADS)

Kim, Dae Ho; Kim, Jin Min

2012-09-01

A conserved discrete model on the Sierpinski gasket substrate is studied. The interface width W in the model follows the Family-Vicsek dynamic scaling form with growth exponent β ≈ 0.0542, roughness exponent α ≈ 0.240 and dynamic exponent z ≈ 4.42. They satisfy a scaling relation α + z = 2zrw, where zrw is the random walk exponent of the fractal substrate. Also, they are in a good agreement with the predicted values of a fractional Langevin equation \\frac{\\partial h}{\\partial t}={\

L1-Based Approximations of PDEs and Applications

DTIC Science & Technology

2012-09-05

the analysis of the Navier-Stokes equations. The early versions of artificial vis- cosities being overly dissipative, the interest for these technique ...Guermond, and B. Popov. Stability analysis of explicit en- tropy viscosity methods for non-linear scalar conservation equations. Math. Comp., 2012... methods for solv- ing mathematical models of nonlinear phenomena such as nonlinear conservation laws, surface/image/data reconstruction problems

Non-dispersive conservative regularisation of nonlinear shallow water (and isentropic Euler equations)

NASA Astrophysics Data System (ADS)

Clamond, Didier; Dutykh, Denys

2018-02-01

A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and posses a variational structure; thus, the mass, the momentum and the energy are conserved. Hence, for instance, regularised hydraulic jumps are smooth and non-oscillatory. Another particularly interesting feature of this regularisation is that smoothed 'shocks' propagates at exactly the same speed as the original discontinuous ones. The performance of the new model is illustrated numerically on some dam-break test cases, which are classical in the hyperbolic realm.

Multi-Hamiltonian structure of the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Arik, Metin; Neyzi, Fahrünisa; Nutku, Yavuz; Olver, Peter J.; Verosky, John M.

1989-06-01

The multi-Hamiltonian structure, conservation laws, and higher order symmetries for the Born-Infeld equation are exhibited. A new transformation of the Born-Infeld equation to the equations of a Chaplygin gas is presented and explored. The Born-Infeld equation is distinguished among two-dimensional hyperbolic systems by its wealth of such multi-Hamiltonian structures.

Frequency modulation at a moving material interface and a conservation law for wave number. [acoustic wave reflection and transmission

NASA Technical Reports Server (NTRS)

Kleinstein, G. G.; Gunzburger, M. D.

1976-01-01

An integral conservation law for wave numbers is considered. In order to test the validity of the proposed conservation law, a complete solution for the reflection and transmission of an acoustic wave impinging normally on a material interface moving at a constant speed is derived. The agreement between the frequency condition thus deduced from the dynamic equations of motion and the frequency condition derived from the jump condition associated with the integral equation supports the proposed law as a true conservation law. Additional comparisons such as amplitude discontinuities and Snells' law in a moving media further confirm the stated proposition. Results are stated concerning frequency and wave number relations across a shock front as predicted by the proposed conservation law.

Dynamic renormalization-group analysis of the d+1 dimensional Kuramoto-Sivashinsky equation with both conservative and nonconservative noises

NASA Astrophysics Data System (ADS)

Zhang, L.; Tang, G.; Xun, Z.; Han, K.; Chen, H.; Hu, B.

2008-05-01

The long-wavelength properties of the (d + 1)-dimensional Kuramoto-Sivashinsky (KS) equation with both conservative and nonconservative noises are investigated by use of the dynamic renormalization-group (DRG) theory. The dynamic exponent z and roughness exponent α are calculated for substrate dimensions d = 1 and d = 2, respectively. In the case of d = 1, we arrive at the critical exponents z = 1.5 and α = 0.5 , which are consistent with the results obtained by Ueno et al. in the discussion of the same noisy KS equation in 1+1 dimensions [Phys. Rev. E 71, 046138 (2005)] and are believed to be identical with the dynamic scaling of the Kardar-Parisi-Zhang (KPZ) in 1+1 dimensions. In the case of d = 2, we find a fixed point with the dynamic exponents z = 2.866 and α = -0.866 , which show that, as in the 1 + 1 dimensions situation, the existence of the conservative noise in 2 + 1 or higher dimensional KS equation can also lead to new fixed points with different dynamic scaling exponents. In addition, since a higher order approximation is adopted, our calculations in this paper have improved the results obtained previously by Cuerno and Lauritsen [Phys. Rev. E 52, 4853 (1995)] in the DRG analysis of the noisy KS equation, where the conservative noise is not taken into account.

Discrete Variational Approach for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, J. Paxon; Shadwick, B. A.

2014-10-01

The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.

Periodic motions of generalized conservative mechanical systems whose equations of motion contain a large parameter

NASA Astrophysics Data System (ADS)

Sazonov, V. V.

An analysis is made of a generalized conservative mechanical system whose equations of motion contain a large parameter characterizing local forces acting along certain generalized coordinates. It is shown that the equations have periodic solutions which are close to periodic solutions to the corresponding degenerate equations. As an example, the periodic motions of a satellite with respect to its center of mass due to gravitational and restoring aerodynamic moments are examined for the case where the aerodynamic moment is much larger than the gravitational moment. Such motions can be treated as nominal unperturbed motions of a satellite under conditions of single-axis aerodynamic attitude control.

Thermally Driven One-Fluid Electron-Proton Solar Wind: Eight-Moment Approximation

NASA Astrophysics Data System (ADS)

Olsen, Espen Lyngdal; Leer, Egil

1996-05-01

In an effort to improve the "classical" solar wind model, we study an eight-moment approximation hydrodynamic solar wind model, in which the full conservation equation for the heat conductive flux is solved together with the conservation equations for mass, momentum, and energy. We consider two different cases: In one model the energy flux needed to drive the solar wind is supplied as heat flux from a hot coronal base, where both the density and temperature are specified. In the other model, the corona is heated. In that model, the coronal base density and temperature are also specified, but the temperature increases outward from the coronal base due to a specified energy flux that is dissipated in the corona. The eight-moment approximation solutions are compared with the results from a "classical" solar wind model in which the collision-dominated gas expression for the heat conductive flux is used. It is shown that the "classical" expression for the heat conductive flux is generally not valid in the solar wind. In collisionless regions of the flow, the eight-moment approximation gives a larger thermalization of the heat conductive flux than the models using the collision-dominated gas approximation for the heat flux, but the heat flux is still larger than the "saturation heat flux." This leads to a breakdown of the electron distribution function, which turns negative in the collisionless region of the flow. By increasing the interaction between the electrons, the heat flux is reduced, and a reasonable shape is obtained on the distribution function. By solving the full set of equations consistent with the eight-moment distribution function for the electrons, we are thus able to draw inferences about the validity of the eight-moment description of the solar wind as well as the validity of the very commonly used collision-dominated gas approximation for the heat conductive flux in the solar wind.

Computer program for calculating full potential transonic, quasi-three-dimensional flow through a rotating turbomachinery blade row

NASA Technical Reports Server (NTRS)

Farrell, C. A.

1982-01-01

A fast, reliable computer code is described for calculating the flow field about a cascade of arbitrary two dimensional airfoils. The method approximates the three dimensional flow in a turbomachinery blade row by correcting for stream tube convergence and radius change in the throughflow direction. A fully conservative solution of the full potential equation is combined with the finite volume technique on a body-fitted periodic mesh, with an artificial density imposed in the transonic region to insure stability and the capture of shock waves. The instructions required to set up and use the code are included. The name of the code is QSONIC. A numerical example is also given to illustrate the output of the program.

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

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

Gamba, Irene M.; ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712; Haack, Jeffrey R.

2014-08-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit tomore » the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.« less

Lie Symmetry Analysis, Conservation Laws and Exact Power Series Solutions for Time-Fractional Fordy-Gibbons Equation

NASA Astrophysics Data System (ADS)

Feng, Lian-Li; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian

2016-09-01

In this paper, the time fractional Fordy-Gibbons equation is investigated with Riemann-Liouville derivative. The equation can be reduced to the Caudrey-Dodd-Gibbon equation, Savada-Kotera equation and the Kaup-Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method. Supported by the Fundamental Research Funds for Key Discipline Construction under Grant No. XZD201602, the Fundamental Research Funds for the Central Universities under Grant Nos. 2015QNA53 and 2015XKQY14, the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Mines, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2015M570498, and Natural Sciences Foundation of China under Grant No. 11301527

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

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

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

DOE PAGES

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris; ...

2016-04-22

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods - Part 1: Derivation and properties

NASA Astrophysics Data System (ADS)

Eldred, Christopher; Randall, David

2017-02-01

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.

A simple mass-conserved level set method for simulation of multiphase flows

NASA Astrophysics Data System (ADS)

Yuan, H.-Z.; Shu, C.; Wang, Y.; Shu, S.

2018-04-01

In this paper, a modified level set method is proposed for simulation of multiphase flows with large density ratio and high Reynolds number. The present method simply introduces a source or sink term into the level set equation to compensate the mass loss or offset the mass increase. The source or sink term is derived analytically by applying the mass conservation principle with the level set equation and the continuity equation of flow field. Since only a source term is introduced, the application of the present method is as simple as the original level set method, but it can guarantee the overall mass conservation. To validate the present method, the vortex flow problem is first considered. The simulation results are compared with those from the original level set method, which demonstrates that the modified level set method has the capability of accurately capturing the interface and keeping the mass conservation. Then, the proposed method is further validated by simulating the Laplace law, the merging of two bubbles, a bubble rising with high density ratio, and Rayleigh-Taylor instability with high Reynolds number. Numerical results show that the mass is a well-conserved by the present method.

A new flux-conserving numerical scheme for the steady, incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.

1994-01-01

This paper is concerned with the continued development of a new numerical method, the space-time solution element (STS) method, for solving conservation laws. The present work focuses on the two-dimensional, steady, incompressible Navier-Stokes equations. Using first an integral approach, and then a differential approach, the discrete flux conservation equations presented in a recent paper are rederived. Here a simpler method for determining the flux expressions at cell interfaces is given; a systematic and rigorous derivation of the conditions used to simulate the differential form of the governing conservation law(s) is provided; necessary and sufficient conditions for a discrete approximation to satisfy a conservation law in E2 are derived; and an estimate of the local truncation error is given. A specific scheme is then constructed for the solution of the thin airfoil boundary layer problem. Numerical results are presented which demonstrate the ability of the scheme to accurately resolve the developing boundary layer and wake regions using grids which are much coarser than those employed by other numerical methods. It is shown that ten cells in the cross-stream direction are sufficient to accurately resolve the developing airfoil boundary layer.

Couplings of gravitational currents with Chern-Simons gravities

NASA Astrophysics Data System (ADS)

Ertem, Ümit; Açık, Özgür

2013-02-01

The coupling of conserved p-brane currents with non-Abelian gauge theories is done consistently by using Chern-Simons forms. Conserved currents localized on p-branes that have a gravitational origin can be constructed from Killing-Yano forms of the underlying spacetime. We propose a generalization of the coupling procedure with Chern-Simons gravities to the case of gravitational conserved currents. In odd dimensions, the field equations of coupled Chern-Simons gravities that describe the local curvature on p-branes are obtained. In special cases of three and five dimensions, the field equations are investigated in detail.

Divergent conservation laws in hyperbolic thermoelasticity

NASA Astrophysics Data System (ADS)

Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present study is devoted to the problem of formulation of conservation laws in divergent form for hyperbolic thermoelastic continua. The field formalism is applied to study the problem. A natural density of thermoelastic action and the corresponding variational least action principle are formulated. A special form of the first variation of the action is employed to obtain 4-covariant divergent conservation laws. Differential field equations and constitutive laws are derived from a special form of the first variation of the action integral. The objectivity of constitutive equations is provided by the rotationally invariant forms of the Lagrangian employed.

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

NASA Technical Reports Server (NTRS)

Hu, Fang; Pizzo, Michelle E.; Nark, Douglas M.

2017-01-01

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Direct numerical simulations of fluid flow, heat transfer and phase changes

NASA Technical Reports Server (NTRS)

Juric, D.; Tryggvason, G.; Han, J.

1997-01-01

Direct numerical simulations of fluid flow, heat transfer, and phase changes are presented. The simulations are made possible by a recently developed finite difference/front tracking method based on the one-field formulation of the governing equations where a single set of conservation equations is written for all the phases involved. The conservation equations are solved on a fixed rectangular grid, but the phase boundaries are kept sharp by tracking them explicitly by a moving grid of lower dimension. The method is discussed and applications to boiling heat transfer and the solidification of drops colliding with a wall are shown.

Applications of a Property of the Schrödinger Equation to the Modeling of Conservative Discrete Systems

NASA Astrophysics Data System (ADS)

Popa, Alexandru

1998-08-01

Recently we have demonstrated in a mathematical paper the following property: The energy which results from the Schrödinger equation can be rigorously calculated by line integrals of analytical functions, if the Hamilton-Jacobi equation, written for the same system, is satisfied in the space of coordinates by a periodical trajectory. We present now an accurate analysis model of the conservative discrete systems, that is based on this property. The theory is checked for a lot of atomic systems. The experimental data, which are ionization energies, are taken from well known books.

Energy conservation and H theorem for the Enskog-Vlasov equation

NASA Astrophysics Data System (ADS)

Benilov, E. S.; Benilov, M. S.

2018-06-01

The Enskog-Vlasov (EV) equation is a widely used semiphenomenological model of gas-liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.

A low-dispersion, exactly energy-charge-conserving semi-implicit relativistic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Luis, Chacon; Bird, Robert; Stark, David; Yin, Lin; Albright, Brian

2017-10-01

Leap-frog based explicit algorithms, either ``energy-conserving'' or ``momentum-conserving'', do not conserve energy discretely. Time-centered fully implicit algorithms can conserve discrete energy exactly, but introduce large dispersion errors in the light-wave modes, regardless of timestep sizes. This can lead to intolerable simulation errors where highly accurate light propagation is needed (e.g. laser-plasma interactions, LPI). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce a low-dispersion, exactly energy-and-charge-conserving PIC algorithm. Specifically, we employ the leap-frog method for Maxwell equations, and the Crank-Nicolson method for particle equations. Such an algorithm admits exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm has been implemented in a code named iVPIC, based on the VPIC code developed at LANL. We will present numerical results that demonstrate the properties of the scheme with sample test problems (e.g. Weibel instability run for 107 timesteps, and LPI applications.

Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity

NASA Astrophysics Data System (ADS)

Feijoo, David; Zezyulin, Dmitry A.; Konotop, Vladimir V.

2015-12-01

We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT ) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT -symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT -symmetric cases. Interactions and collisions between the conservative and PT -symmetric solitons are briefly investigated, as well.

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2014-10-01

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation to Maxwell's equations, which avoids radiative noise issues by ordering out the light wave. An implicit, orbit-averaged, time-space-centered finite difference scheme is employed in both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. We have developed a simple preconditioner that targets electrostatic waves and skin currents, and allows us to employ time steps O(√{mi /me } c /veT) larger than the explicit CFL. Several 1D numerical experiments demonstrate the accuracy, performance, and conservation properties of the algorithm. In particular, the scheme is shown to be second-order accurate, and CPU speedups of more than three orders of magnitude vs. an explicit Vlasov-Maxwell solver are demonstrated in the "cold" plasma regime (where kλD ≪ 1).

Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

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

Cruz, Hans, E-mail: hans@ciencias.unam.mx; Schuch, Dieter; Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx

2015-09-15

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

Lie symmetry analysis, conservation laws, solitary and periodic waves for a coupled Burger equation

NASA Astrophysics Data System (ADS)

Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Zhang, Tian-Tian

2017-01-01

Under investigation in this paper is a generalized (2 + 1)-dimensional coupled Burger equation with variable coefficients, which describes lots of nonlinear physical phenomena in geophysical fluid dynamics, condense matter physics and lattice dynamics. By employing the Lie group method, the symmetry reductions and exact explicit solutions are obtained, respectively. Based on a direct method, the conservations laws of the equation are also derived. Furthermore, by virtue of the Painlevé analysis, we successfully obtain the integrable condition on the variable coefficients, which plays an important role in further studying the integrability of the equation. Finally, its auto-Bäcklund transformation as well as some new analytic solutions including solitary and periodic waves are also presented via algebraic and differential manipulation.

RAZORBACK - A Research Reactor Transient Analysis Code Version 1.0 - Volume 3: Verification and Validation Report.

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

Talley, Darren G.

2017-04-01

This report describes the work and results of the verification and validation (V&V) of the version 1.0 release of the Razorback code. Razorback is a computer code designed to simulate the operation of a research reactor (such as the Annular Core Research Reactor (ACRR)) by a coupled numerical solution of the point reactor kinetics equations, the energy conservation equation for fuel element heat transfer, the equation of motion for fuel element thermal expansion, and the mass, momentum, and energy conservation equations for the water cooling of the fuel elements. This V&V effort was intended to confirm that the code showsmore » good agreement between simulation and actual ACRR operations.« less

The charge conserving Poisson-Boltzmann equations: Existence, uniqueness, and maximum principle

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

Lee, Chiun-Chang, E-mail: chlee@mail.nhcue.edu.tw

2014-05-15

The present article is concerned with the charge conserving Poisson-Boltzmann (CCPB) equation in high-dimensional bounded smooth domains. The CCPB equation is a Poisson-Boltzmann type of equation with nonlocal coefficients. First, under the Robin boundary condition, we get the existence of weak solutions to this equation. The main approach is variational, based on minimization of a logarithm-type energy functional. To deal with the regularity of weak solutions, we establish a maximum modulus estimate for the standard Poisson-Boltzmann (PB) equation to show that weak solutions of the CCPB equation are essentially bounded. Then the classical solutions follow from the elliptic regularity theorem.more » Second, a maximum principle for the CCPB equation is established. In particular, we show that in the case of global electroneutrality, the solution achieves both its maximum and minimum values at the boundary. However, in the case of global non-electroneutrality, the solution may attain its maximum value at an interior point. In addition, under certain conditions on the boundary, we show that the global non-electroneutrality implies pointwise non-electroneutrality.« less

A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces

NASA Astrophysics Data System (ADS)

Henry de Frahan, Marc T.; Varadan, Sreenivas; Johnsen, Eric

2015-01-01

Although the Discontinuous Galerkin (DG) method has seen widespread use for compressible flow problems in a single fluid with constant material properties, it has yet to be implemented in a consistent fashion for compressible multiphase flows with shocks and interfaces. Specifically, it is challenging to design a scheme that meets the following requirements: conservation, high-order accuracy in smooth regions and non-oscillatory behavior at discontinuities (in particular, material interfaces). Following the interface-capturing approach of Abgrall [1], we model flows of multiple fluid components or phases using a single equation of state with variable material properties; discontinuities in these properties correspond to interfaces. To represent compressible phenomena in solids, liquids, and gases, we present our analysis for equations of state belonging to the Mie-Grüneisen family. Within the DG framework, we propose a conservative, high-order accurate, and non-oscillatory limiting procedure, verified with simple multifluid and multiphase problems. We show analytically that two key elements are required to prevent spurious pressure oscillations at interfaces and maintain conservation: (i) the transport equation(s) describing the material properties must be solved in a non-conservative weak form, and (ii) the suitable variables must be limited (density, momentum, pressure, and appropriate properties entering the equation of state), coupled with a consistent reconstruction of the energy. Further, we introduce a physics-based discontinuity sensor to apply limiting in a solution-adaptive fashion. We verify this approach with one- and two-dimensional problems with shocks and interfaces, including high pressure and density ratios, for fluids obeying different equations of state to illustrate the robustness and versatility of the method. The algorithm is implemented on parallel graphics processing units (GPU) to achieve high speedup.

A GENERAL MASS-CONSERVATIVE NUMERICAL SOLUTION FOR THE UNSATURATED FLOW EQUATION

EPA Science Inventory

Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, ch...

A combined direct/inverse three-dimensional transonic wing design method for vector computers

NASA Technical Reports Server (NTRS)

Weed, R. A.; Carlson, L. A.; Anderson, W. K.

1984-01-01

A three-dimensional transonic-wing design algorithm for vector computers is developed, and the results of sample computations are presented graphically. The method incorporates the direct/inverse scheme of Carlson (1975), a Cartesian grid system with boundary conditions applied at a mean plane, and a potential-flow solver based on the conservative form of the full potential equation and using the ZEBRA II vectorizable solution algorithm of South et al. (1980). The accuracy and consistency of the method with regard to direct and inverse analysis and trailing-edge closure are verified in the test computations.

Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations

NASA Technical Reports Server (NTRS)

Abramopoulos, Frank

1988-01-01

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

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.

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

NASA Technical Reports Server (NTRS)

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

2001-01-01

A method of minimizing numerical errors, and improving nonlinear stability and accuracy associated with low Mach number computational aeroacoustics (CAA) is proposed. The method consists of two levels. From the governing equation level, we condition the Euler equations in two steps. The first step is to split the inviscid flux derivatives into a conservative and a non-conservative portion that satisfies a so called generalized energy estimate. This involves the symmetrization of the Euler equations via a transformation of variables that are functions of the physical entropy. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the second step is to reformulate the split Euler equations in perturbation form with the new unknowns as the small changes of the conservative variables with respect to their large stagnation values. From the numerical scheme level, a stable sixth-order central interior scheme with a third-order boundary schemes that satisfies the discrete analogue of the integration-by-parts procedure used in the continuous energy estimate (summation-by-parts property) is employed.

A Computer Program for the Calculation of Three-Dimensional Transonic Nacelle/Inlet Flowfields

NASA Technical Reports Server (NTRS)

Vadyak, J.; Atta, E. H.

1983-01-01

A highly efficient computer analysis was developed for predicting transonic nacelle/inlet flowfields. This algorithm can compute the three dimensional transonic flowfield about axisymmetric (or asymmetric) nacelle/inlet configurations at zero or nonzero incidence. The flowfield is determined by solving the full-potential equation in conservative form on a body-fitted curvilinear computational mesh. The difference equations are solved using the AF2 approximate factorization scheme. This report presents a discussion of the computational methods used to both generate the body-fitted curvilinear mesh and to obtain the inviscid flow solution. Computed results and correlations with existing methods and experiment are presented. Also presented are discussions on the organization of the grid generation (NGRIDA) computer program and the flow solution (NACELLE) computer program, descriptions of the respective subroutines, definitions of the required input parameters for both algorithms, a brief discussion on interpretation of the output, and sample cases to illustrate application of the analysis.

Stability: Conservation laws, Painlevé analysis and exact solutions for S-KP equation in coupled dusty plasma

NASA Astrophysics Data System (ADS)

EL-Kalaawy, O. H.; Moawad, S. M.; Wael, Shrouk

The propagation of nonlinear waves in unmagnetized strongly coupled dusty plasma with Boltzmann distributed electrons, iso-nonthermal distributed ions and negatively charged dust grains is considered. The basic set of fluid equations is reduced to the Schamel Kadomtsev-Petviashvili (S-KP) equation by using the reductive perturbation method. The variational principle and conservation laws of S-KP equation are obtained. It is shown that the S-KP equation is non-integrable using Painlevé analysis. A set of new exact solutions are obtained by auto-Bäcklund transformations. The stability analysis is discussed for the existence of dust acoustic solitary waves (DASWs) and it is found that the physical parameters have strong effects on the stability criterion. In additional to, the electric field and the true Mach number of this solution are investigated. Finally, we will study the physical meanings of solutions.

f(R)-gravity from Killing tensors

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos

2016-04-01

We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.

Kinetic theory of oxygen isotopic exchange between minerals and water

USGS Publications Warehouse

Criss, R.E.; Gregory, R.T.; Taylor, H.P.

1987-01-01

Kinetic and mass conservation equations are used to describe oxygen isotopic exchange between minerals and water in "closed" and open hydrothermal systems. In cases where n coexisting mineral phases having different reaction rates are present, the exchange process is described by a system of n + 1 simultaneous differential equations consisting of n pseudo first-order rate equations and a conservation of mass equation. The simultaneous solutions to these equations generate curved exchange trajectories on ??-?? plots. Families of such trajectories generated under conditions allowing for different fluid mole fractions, different fluid isotopic compositions, or different fluid flow rates are connected by positive-sloped isochronous lines. These isochrons reproduce the effects observed in hydrothermally exchanged mineral pairs including 1) steep positive slopes, 2) common reversals in the measured fractionation factors (??), and 3) measured fractionations that are highly variable over short distances where no thermal gradient can be geologically demonstrated. ?? 1987.

Current-Voltage and Floating-Potential characteristics of cylindrical emissive probes from a full-kinetic model based on the orbital motion theory

NASA Astrophysics Data System (ADS)

Chen, Xin; Sánchez-Arriaga, Gonzalo

2018-02-01

To model the sheath structure around an emissive probe with cylindrical geometry, the Orbital-Motion theory takes advantage of three conserved quantities (distribution function, transverse energy, and angular momentum) to transform the stationary Vlasov-Poisson system into a single integro-differential equation. For a stationary collisionless unmagnetized plasma, this equation describes self-consistently the probe characteristics. By solving such an equation numerically, parametric analyses for the current-voltage (IV) and floating-potential (FP) characteristics can be performed, which show that: (a) for strong emission, the space-charge effects increase with probe radius; (b) the probe can float at a positive potential relative to the plasma; (c) a smaller probe radius is preferred for the FP method to determine the plasma potential; (d) the work function of the emitting material and the plasma-ion properties do not influence the reliability of the floating-potential method. Analytical analysis demonstrates that the inflection point of an IV curve for non-emitting probes occurs at the plasma potential. The flat potential is not a self-consistent solution for emissive probes.

Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

NASA Astrophysics Data System (ADS)

Moatssime, H. Al; Esselaoui, D.; Hakim, A.; Raghay, S.

2001-08-01

This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss-Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright

TEMPEST. Transient 3-D Thermal-Hydraulic

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

Eyler, L.L.

TEMPEST is a transient, three-dimensional, hydrothermal program that is designed to analyze a range of coupled fluid dynamic and heat transfer systems of particular interest to the Fast Breeder Reactor (FBR) thermal-hydraulic design community. The full three-dimensional, time-dependent equations of motion, continuity, and heat transport are solved for either laminar or turbulent fluid flow, including heat diffusion and generation in both solid and liquid materials. The equations governing mass, momentum, and energy conservation for incompressible flows and small density variations (Boussinesq approximation) are solved using finite-difference techniques. Analyses may be conducted in either cylindrical or Cartesian coordinate systems. Turbulence ismore » treated using a two-equation model. Two auxiliary plotting programs, SEQUEL and MANPLOT, for use with TEMPEST output are included. SEQUEL may be operated in batch or interactive mode; it generates data required for vector plots, contour plots of scalar quantities, line plots, grid and boundary plots, and time-history plots. MANPLOT reads the SEQUEL-generated data and creates the hardcopy plots. TEMPEST can be a valuable hydrothermal design analysis tool in areas outside the intended FBR thermal-hydraulic design community.« less

A full potential inverse method based on a density linearization scheme for wing design

NASA Technical Reports Server (NTRS)

Shankar, V.

1982-01-01

A mixed analysis inverse procedure based on the full potential equation in conservation form was developed to recontour a given base wing to produce density linearization scheme in applying the pressure boundary condition in terms of the velocity potential. The FL030 finite volume analysis code was modified to include the inverse option. The new surface shape information, associated with the modified pressure boundary condition, is calculated at a constant span station based on a mass flux integration. The inverse method is shown to recover the original shape when the analysis pressure is not altered. Inverse calculations for weakening of a strong shock system and for a laminar flow control (LFC) pressure distribution are presented. Two methods for a trailing edge closure model are proposed for further study.

Structure-preserving operators for thermal-nonequilibrium hydrodynamics

NASA Astrophysics Data System (ADS)

Shiroto, Takashi; Kawai, Soshi; Ohnishi, Naofumi

2018-07-01

Radiation hydrodynamics simulations based on a single fluid two-temperature model may violate the law of energy conservation, because the governing equations are expressed in a nonconservative formulation. In this study, we maintain the important physical requirements by employing a strategy based on the key concept that mathematical structures associated with conservative and nonconservative equations are preserved, even at the discrete level. To this end, we discretize the conservation laws and transform them using exact algebraic operations. The proposed scheme maintains global conservation errors within the round-off level. In addition, a numerical experiment concerning the shock tube problem suggests that the proposed scheme agrees well with the jump conditions at the discontinuities regulated by the Rankine-Hugoniot relationship. The generalized derivation allows us to employ arbitrary central difference, artificial dissipation, and Runge-Kutta methods.

A Numerical Model for Trickle Bed Reactors

NASA Astrophysics Data System (ADS)

Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

2000-12-01

Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

A new multi-symplectic scheme for the generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Li, Haochen; Sun, Jianqiang

2012-09-01

We propose a new scheme for the generalized Kadomtsev-Petviashvili (KP) equation. The multi-symplectic conservation property of the new scheme is proved. Back error analysis shows that the new multi-symplectic scheme has second order accuracy in space and time. Numerical application on studying the KPI equation and the KPII equation are presented in detail.

Steady inviscid transonic flows over planar airfoils: A search for a simplified procedure

NASA Technical Reports Server (NTRS)

Magnus, R.; Yoshihara, H.

1973-01-01

A finite difference procedure based upon a system of unsteady equations in proper conservation form with either exact or small disturbance steady terms is used to calculate the steady flows over several classes of airfoils. The airfoil condition is fulfilled on a slab whose upstream extremity is a semi-circle overlaying the airfoil leading edge circle. The limitations of the small disturbance equations are demonstrated in an extreme example of a blunt-nosed, aft-cambered airfoil. The necessity of using the equations in proper conservation form to capture the shock properly is stressed. Ability of the steady relaxation procedures to capture the shock is briefly examined.

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Thomas, J. L.

2000-01-01

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Relativistic fluid dynamics with spin

NASA Astrophysics Data System (ADS)

Florkowski, Wojciech; Friman, Bengt; Jaiswal, Amaresh; Speranza, Enrico

2018-04-01

Using the conservation laws for charge, energy, momentum, and angular momentum, we derive hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the polarization tensor, starting from local equilibrium distribution functions for particles and antiparticles with spin 1/2. The resulting set of differential equations extends the standard picture of perfect-fluid hydrodynamics with a conserved entropy current in a minimal way. This framework can be used in space-time analyses of the evolution of spin and polarization in various physical systems including high-energy nuclear collisions. We demonstrate that a stationary vortex, which exhibits vorticity-spin alignment, corresponds to a special solution of the spin-hydrodynamical equations.

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

NASA Technical Reports Server (NTRS)

Gordnier, R. E.; Rubin, S. G.

1986-01-01

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

Variational principles for relativistic smoothed particle hydrodynamics

NASA Astrophysics Data System (ADS)

Monaghan, J. J.; Price, D. J.

2001-12-01

In this paper we show how the equations of motion for the smoothed particle hydrodynamics (SPH) method may be derived from a variational principle for both non-relativistic and relativistic motion when there is no dissipation. Because the SPH density is a function of the coordinates the derivation of the equations of motion through variational principles is simpler than in the continuum case where the density is defined through the continuity equation. In particular, the derivation of the general relativistic equations is more direct and simpler than that of Fock. The symmetry properties of the Lagrangian lead immediately to the familiar additive conservation laws of linear and angular momentum and energy. In addition, we show that there is an approximately conserved quantity which, in the continuum limit, is the circulation.

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods $-$ Part 1: Derivation and properties

DOE PAGES

Eldred, Christopher; Randall, David

2017-02-17

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restrictedmore » to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Lastly, detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.« less

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

Jibben, Zechariah Joel; Herrmann, Marcus

Here, we present a Runge-Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constantmore » with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.« less

Variational objective analysis for cyclone studies

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.

1989-01-01

Significant accomplishments during 1987 to 1988 are summarized with regard to each of the major project components. Model 1 requires satisfaction of two nonlinear horizontal momentum equations, the integrated continuity equation, and the hydrostatic equation. Model 2 requires satisfaction of model 1 plus the thermodynamic equation for a dry atmosphere. Model 3 requires satisfaction of model 2 plus the radiative transfer equation. Model 4 requires satisfaction of model 3 plus a moisture conservation equation and a parameterization for moist processes.

Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

NASA Astrophysics Data System (ADS)

Gumral, Hasan

Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

NASA Astrophysics Data System (ADS)

Zanotti, Olindo; Dumbser, Michael

2016-01-01

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of the cell averages of the conserved quantities. Therefore, our new approach performs the spatial WENO reconstruction twice: the first WENO reconstruction is carried out on the known cell averages of the conservative variables. The WENO polynomials are then used at the cell centers to compute point values of the conserved variables, which are subsequently converted into point values of the primitive variables. This is the only place where the conversion from conservative to primitive variables is needed in the new scheme. Then, a second WENO reconstruction is performed on the point values of the primitive variables to obtain piecewise high order reconstruction polynomials of the primitive variables. The reconstruction polynomials are subsequently evolved in time with a novel space-time finite element predictor that is directly applied to the governing PDE written in primitive form. The resulting space-time polynomials of the primitive variables can then be directly used as input for the numerical fluxes at the cell boundaries in the underlying conservative finite volume scheme. Hence, the number of necessary conversions from the conserved to the primitive variables is reduced to just one single conversion at each cell center. We have verified the validity of the new approach over a wide range of hyperbolic systems, including the classical Euler equations of gas dynamics, the special relativistic hydrodynamics (RHD) and ideal magnetohydrodynamics (RMHD) equations, as well as the Baer-Nunziato model for compressible two-phase flows. In all cases we have noticed that the new ADER schemes provide less oscillatory solutions when compared to ADER finite volume schemes based on the reconstruction in conserved variables, especially for the RMHD and the Baer-Nunziato equations. For the RHD and RMHD equations, the overall accuracy is improved and the CPU time is reduced by about 25 %. Because of its increased accuracy and due to the reduced computational cost, we recommend to use this version of ADER as the standard one in the relativistic framework. At the end of the paper, the new approach has also been extended to ADER-DG schemes on space-time adaptive grids (AMR).

Noether symmetries and stability of ideal gas solutions in Galileon cosmology

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Jamal, Sameerah; Leon, Genly; Paliathanasis, Andronikos

2017-03-01

A class of generalized Galileon cosmological models, which can be described by a pointlike Lagrangian, is considered in order to utilize Noether's theorem to determine conservation laws for the field equations. In the Friedmann-Lemaître-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Because of the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability.

Research in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The numerical integration of quasi-one-dimensional unsteady flow problems which involve finite rate chemistry are discussed, and are expressed in terms of conservative form Euler and species conservation equations. Hypersonic viscous calculations for delta wing geometries is also examined. The conical Navier-Stokes equations model was selected in order to investigate the effects of viscous-inviscid interations. The more complete three-dimensional model is beyond the available computing resources. The flux vector splitting method with van Leer's MUSCL differencing is being used. Preliminary results were computed for several conditions.

Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

DOE PAGES

Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong

2015-01-23

In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation

NASA Technical Reports Server (NTRS)

Chuang, Shun-Lien

1987-01-01

Two sets of coupled-mode equations for multiwaveguide systems are derived using a generalized reciprocity relation; one set for a lossless system, and the other for a general lossy or lossless system. The second set of equations also reduces to those of the first set in the lossless case under the condition that the transverse field components are chosen to be real. Analytical relations between the coupling coefficients are shown and applied to the coupling of mode equations. It is shown analytically that these results satisfy exactly both the reciprocity theorem and power conservation. New orthogonal relations between the supermodes are derived in matrix form, with the overlap integrals taken into account.

Geometry of Lax pairs: Particle motion and Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2013-01-01

A geometric formulation of the Lax pair equation on a curved manifold is studied using the phase-space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well-known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting a hidden symmetry of Killing-Yano tensors.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.

PubMed

Shalymov, Dmitry S; Fradkov, Alexander L

2016-01-01

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle

PubMed Central

2016-01-01

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined. PMID:26997886

Three-dimensional elastic wave analysis of the October 2, 2004 tremor at Mount St. Helens, Washington.

NASA Astrophysics Data System (ADS)

Denlinger, R. P.

2006-12-01

On October 2, 2004, three component, broad-frequency band seismometers as far as 250 km away from Mount St. Helens volcano detected a prominent low-frequency resonance associated with the onset of eruptive volcanic activity. The energy is dominantly in the 0.5 to 10 Hz range. Since gas emissions were low, I investigate a gas-free tremor mechanism generated by sudden extension of a pressurized, cylindrical, visco- elastic magma conduit beneath the mountain as it forces its way through a brittle crust. The concept is that rapid faulting of the crust around and above the magma results in a sudden drop in resistance and, consequently, a concurrent extension of the magma in the magma column at a rate greater than magma can resupply the column. The result is a rapid pressure drop in the magma, causing the column to oscillate and radiate elastic energy into the surrounding crust. The full wavefield generated by this physical mechanism is analyzed using the finite volume method of Leveque (2002), with the approximation outlined in Langseth and Leveque (2000) for hyperbolic conservation laws. In this method, the three-dimensional equations of elasticity are written as a first order set of conservation equations, with a solution vector composed of 3 velocity components and 6 stress components. The eigenvectors of the jacobian matrices of these conservation equations are used in a fourth-order Taylors series expansion of the solution vector around a small increment in time. This method is robust, allows waves to cleanly propagate off of a finite computational grid, and includes surface and interface waves. The method also allows for extremely large contrasts in elastic moduli across internal boundaries in the grid, necessary to accommodate the large variations in rigidity between a hot, visco-elastic magma at depth and the Earth's crust. Analyzing the October 2, 2004 tremor observed at Johnson Ridge Observatory, 9 km north of the mountain, for pressure drop in a 10 km long conduit, I obtain 0.3 +/- .05 MPa, which is consistent with elastic analysis of crustal deformation around the mountain during this time period. Langseth, J.O., and R.J. LeVeque, 2000, A wave propagation method for 3D hyperbolic conservation laws, J. Comp. Phys., 165, 126-166. Leveque, R.J., 2002, Finite volume methods for hyperbolic problems, Cambridge U. Press, 558 p.

Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe; Kwak, Dochan; Vinokur, Marcel

1992-01-01

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Numerical viscosity and the entropy condition for conservative difference schemes

NASA Technical Reports Server (NTRS)

Tadmor, E.

1983-01-01

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E schemes - those containing more numerical viscosity than Godunov's scheme.

Quantum asymmetry between time and space

PubMed Central

2016-01-01

An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time, whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental, is represented by equations of motion and conservation laws that operate differently over time and space. If, however, the asymmetry was found to be due to deeper causes, this conventional view of time evolution would need reworking. Here we show, using a sum-over-paths formalism, that a violation of time reversal (T) symmetry might be such a cause. If T symmetry is obeyed, then the formalism treats time and space symmetrically such that states of matter are localized both in space and in time. In this case, equations of motion and conservation laws are undefined or inapplicable. However, if T symmetry is violated, then the same sum over paths formalism yields states that are localized in space and distributed without bound over time, creating an asymmetry between time and space. Moreover, the states satisfy an equation of motion (the Schrödinger equation) and conservation laws apply. This suggests that the time–space asymmetry is not elemental as currently presumed, and that T violation may have a deep connection with time evolution. PMID:26997899

Effects of Nonequilibrium Chemistry and Darcy-Forchheimer Pyrolysis Flow for Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2013-01-01

The fully implicit ablation and thermal response code simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid.This work describes new modeling capabilities that are added to a special version of code. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Two groups of parametric studies of the phenolic impregnated carbon ablator are performed. In the first group, an Orion flight environment for a proposed lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results indicate that the presence of chemical nonequilibrium pyrolysis gas flow does not significantly alter the in-depth thermal response performance predicted using the chemical equilibrium gas model.

A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

NASA Technical Reports Server (NTRS)

Shih, T. I. P.; Yang, S. L.; Schock, H. J.

1986-01-01

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Numerical Simulation of a Solar Domestic Hot Water System

NASA Astrophysics Data System (ADS)

Mongibello, L.; Bianco, N.; Di Somma, M.; Graditi, G.; Naso, V.

2014-11-01

An innovative transient numerical model is presented for the simulation of a solar Domestic Hot Water (DHW) system. The solar collectors have been simulated by using a zerodimensional analytical model. The temperature distributions in the heat transfer fluid and in the water inside the tank have been evaluated by one-dimensional models. The reversion elimination algorithm has been used to include the effects of natural convection among the water layers at different heights in the tank on the thermal stratification. A finite difference implicit scheme has been implemented to solve the energy conservation equation in the coil heat exchanger, and the energy conservation equation in the tank has been solved by using the finite difference Euler implicit scheme. Energy conservation equations for the solar DHW components models have been coupled by means of a home-made implicit algorithm. Results of the simulation performed using as input data the experimental values of the ambient temperature and the solar irradiance in a summer day are presented and discussed.

A two-dimensional numerical study of the flow inside the combustion chamber of a motored rotary engine

NASA Technical Reports Server (NTRS)

Shih, T. I-P.; Yang, S. L.; Schock, H. J.

1986-01-01

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

NASA Astrophysics Data System (ADS)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

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

Sugama, H.; Nunami, M.; Department of Fusion Science, SOKENDAI

Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether's theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novelmore » gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations.« less

Development of monitoring system of helium leakage from canister

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

Toriu, D.; Ushijima, S.; Takeda, H.

2013-07-01

This paper presents a computational method for the helium leakage from a canister. The governing equations for compressible fluids consist of mass conservation equation in Eulerian description, momentum equations and energy equation. The numerical procedures are divided into three phases, advection, diffusion and acoustic phases, and the equations of compressible fluids are discretized with a finite volume method. Thus, the mass conservation law is sufficiently satisfied in the calculation region. In particular, our computational method enables us to predict the change of the temperature distributions around the canister boundaries by calculating the governing equations for the compressible gas flows, whichmore » are leaked out from a slight crack on the canister boundary. In order to confirm the validity of our method, it was applied to the basic problem, 2-dimensional natural convection flows in a rectangular cavity. As a result, it was shown that the naturally convected flows can be reasonably simulated by our method. Furthermore, numerical experiments were conducted for the helium leakage from canister and we derived a close relationship between the inner pressure and the boundary temperature distributions.« less

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

Nonlinear (time domain) and linearized (time and frequency domain) solutions to the compressible Euler equations in conservation law form

NASA Technical Reports Server (NTRS)

Sreenivas, Kidambi; Whitfield, David L.

1995-01-01

Two linearized solvers (time and frequency domain) based on a high resolution numerical scheme are presented. The basic approach is to linearize the flux vector by expressing it as a sum of a mean and a perturbation. This allows the governing equations to be maintained in conservation law form. A key difference between the time and frequency domain computations is that the frequency domain computations require only one grid block irrespective of the interblade phase angle for which the flow is being computed. As a result of this and due to the fact that the governing equations for this case are steady, frequency domain computations are substantially faster than the corresponding time domain computations. The linearized equations are used to compute flows in turbomachinery blade rows (cascades) arising due to blade vibrations. Numerical solutions are compared to linear theory (where available) and to numerical solutions of the nonlinear Euler equations.

Central Upwind Scheme for a Compressible Two-Phase Flow Model

PubMed Central

Ahmed, Munshoor; Saleem, M. Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme. PMID:26039242

Central upwind scheme for a compressible two-phase flow model.

PubMed

Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

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.

Dynamic Studies of Struve Double Stars: STF4 and STF 236AB Appear Gravitationally Bound

NASA Astrophysics Data System (ADS)

Wiley, E. O.; Rica, F. M.

2015-01-01

Dynamics of two Struve double stars, WDS 00099+0827 (STF 4) and WDS 02556+2652 (STF 326 AB) are analyzed using astrometric criteria to determine their natures as gravitationally bound or unbound systems. If gravitationally bound, then observed relative velocity will be within limits according to the orbital energy conservation equation. Full implementation of this criterion was possible because the relative radial velocities as well as proper motions have been estimated. Other physical parameters were taken from literature or estimated using published protocols. Monte Carlo analysis indicates that both pairs have a high probability of being gravitationally bound and thus are long-period binaries.

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; McKinney, Jonathan C.; Tóth, Gábor

2003-05-01

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.

Analysis of viscous transonic flow over airfoil sections

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Wu, Jiunn-Chi; Sankar, L. N.

1987-01-01

A full Navier-Stokes solver has been used to model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to be held at the AIAA 25th Aerospace Sciences Meeting. The NACA 0012, RAE 2822 and Jones airfoils have been investigated for both attached and separated transonic flows. Predictions for pressure distributions, loads, skin friction coefficients, boundary layer displacement thickness and velocity profiles are included and compared with experimental data when possible. Overall, the results are in good agreement with experimental data.

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic method in both the attenuating homogeneous and heterogeneous mediums.

A Model to Couple Flow, Thermal and Reactive Chemical Transport, and Geo-mechanics in Variably Saturated Media

NASA Astrophysics Data System (ADS)

Yeh, G. T.; Tsai, C. H.

2015-12-01

This paper presents the development of a THMC (thermal-hydrology-mechanics-chemistry) process model in variably saturated media. The governing equations for variably saturated flow and reactive chemical transport are obtained based on the mass conservation principle of species transport supplemented with Darcy's law, constraint of species concentration, equation of states, and constitutive law of K-S-P (Conductivity-Degree of Saturation-Capillary Pressure). The thermal transport equation is obtained based on the conservation of energy. The geo-mechanic displacement is obtained based on the assumption of equilibrium. Conventionally, these equations have been implicitly coupled via the calculations of secondary variables based on primary variables. The mechanisms of coupling have not been obvious. In this paper, governing equations are explicitly coupled for all primary variables. The coupling is accomplished via the storage coefficients, transporting velocities, and conduction-dispersion-diffusion coefficient tensor; one set each for every primary variable. With this new system of equations, the coupling mechanisms become clear. Physical interpretations of every term in the coupled equations will be discussed. Examples will be employed to demonstrate the intuition and superiority of these explicit coupling approaches. Keywords: Variably Saturated Flow, Thermal Transport, Geo-mechanics, Reactive Transport.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

NASA Astrophysics Data System (ADS)

Gross, Markus

2018-03-01

A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards–Wilkinson equation with non-conserved noise and the Mullins–Herring equation with conserved noise. The profile is subject to either periodic or Dirichlet (no-flux) boundary conditions. We determine the noise-driven time-evolution of the profile between an initially flat configuration and the instant at which the profile reaches a given height M for the first time. The shape of the averaged profile agrees well with the prediction of weak-noise theory (WNT), which describes the most-likely trajectory to a fixed first-passage time. Furthermore, in agreement with WNT, on average the profile approaches the height M algebraically in time, with an exponent that is essentially independent of the boundary conditions. However, the actual value of the dynamic exponent turns out to be significantly smaller than predicted by WNT. This ‘renormalization’ of the exponent is explained in terms of the entropic repulsion exerted by the impenetrable boundary on the fluctuations of the profile around its most-likely path. The entropic repulsion mechanism is analyzed in detail for a single (fractional) Brownian walker, which describes the anomalous diffusion of a tagged monomer of the interface as it approaches the absorbing boundary. The present study sheds light on the accuracy and the limitations of the weak-noise approximation for the description of the full first-passage dynamics.

SPH non-Newtonian Model for Ice Sheet and Ice Shelf Dynamics

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

Tartakovsky, Alexandre M.; Pan, Wenxiao; Monaghan, Joseph J.

2012-07-07

We propose a new three-dimensional smoothed particle hydrodynamics (SPH) non-Newtonian model to study coupled ice sheet and ice shelf dynamics. Most existing ice sheet numerical models use a grid-based Eulerian approach, and are usually restricted to shallow ice sheet and ice shelf approximations of the momentum conservation equation. SPH, a fully Lagrangian particle method, solves the full momentum conservation equation. SPH method also allows modeling of free-surface flows, large material deformation, and material fragmentation without employing complex front-tracking schemes, and does not require re-meshing. As a result, SPH codes are highly scalable. Numerical accuracy of the proposed SPH model ismore » first verified by simulating a plane shear flow with a free surface and the propagation of a blob of ice along a horizontal surface. Next, the SPH model is used to investigate the grounding line dynamics of ice sheet/shelf. The steady position of the grounding line, obtained from our SPH simulations, is in good agreement with laboratory observations for a wide range of bedrock slopes, ice-to-fluid density ratios, and flux. We examine the effect of non-Newtonian behavior of ice on the grounding line dynamics. The non-Newtonian constitutive model is based on Glen's law for a creeping flow of a polycrystalline ice. Finally, we investigate the effect of a bedrock geometry on a steady-state position of the grounding line.« less

Conservation laws with coinciding smooth solutions but different conserved variables

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Guerra, Graziano

2018-04-01

Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

Optical solitons, nonlinear self-adjointness and conservation laws for the cubic nonlinear Shrödinger's equation with repulsive delta potential

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-11-01

In this paper, the complex envelope function ansatz method is used to acquire the optical solitons to the cubic nonlinear Shrödinger's equation with repulsive delta potential (δ-NLSE). The method reveals dark and bright optical solitons. The necessary constraint conditions which guarantee the existence of the solitons are also presented. We studied the δ-NLSE by analyzing a system of partial differential equations (PDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system and prove that the system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conserved vectors for the system using the general Cls theorem presented by Ibragimov. Some interesting figures for the acquired solutions are also presented.

SCORE-EVET: a computer code for the multidimensional transient thermal-hydraulic analysis of nuclear fuel rod arrays. [BWR; PWR

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

Benedetti, R. L.; Lords, L. V.; Kiser, D. M.

1978-02-01

The SCORE-EVET code was developed to study multidimensional transient fluid flow in nuclear reactor fuel rod arrays. The conservation equations used were derived by volume averaging the transient compressible three-dimensional local continuum equations in Cartesian coordinates. No assumptions associated with subchannel flow have been incorporated into the derivation of the conservation equations. In addition to the three-dimensional fluid flow equations, the SCORE-EVET code ocntains: (a) a one-dimensional steady state solution scheme to initialize the flow field, (b) steady state and transient fuel rod conduction models, and (c) comprehensive correlation packages to describe fluid-to-fuel rod interfacial energy and momentum exchange. Velocitymore » and pressure boundary conditions can be specified as a function of time and space to model reactor transient conditions such as a hypothesized loss-of-coolant accident (LOCA) or flow blockage.« less

Lie Symmetry Analysis and Conservation Laws of a Generalized Time Fractional Foam Drainage Equation

NASA Astrophysics Data System (ADS)

Wang, Li; Tian, Shou-Fu; Zhao, Zhen-Tao; Song, Xiao-Qiu

2016-07-01

In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann—Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method. Supported by the National Training Programs of Innovation and Entrepreneurship for Undergraduates under Grant No. 201410290039, the Fundamental Research Funds for the Central Universities under Grant Nos. 2015QNA53 and 2015XKQY14, the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Mines, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2015M570498, and Natural Sciences Foundation of China under Grant No. 11301527

The development of flux-split algorithms for flows with non-equilibrium thermodynamics and chemical reactions

NASA Technical Reports Server (NTRS)

Grossman, B.; Cinella, P.

1988-01-01

A finite-volume method for the numerical computation of flows with nonequilibrium thermodynamics and chemistry is presented. A thermodynamic model is described which simplifies the coupling between the chemistry and thermodynamics and also results in the retention of the homogeneity property of the Euler equations (including all the species continuity and vibrational energy conservation equations). Flux-splitting procedures are developed for the fully coupled equations involving fluid dynamics, chemical production and thermodynamic relaxation processes. New forms of flux-vector split and flux-difference split algorithms are embodied in a fully coupled, implicit, large-block structure, including all the species conservation and energy production equations. Several numerical examples are presented, including high-temperature shock tube and nozzle flows. The methodology is compared to other existing techniques, including spectral and central-differenced procedures, and favorable comparisons are shown regarding accuracy, shock-capturing and convergence rates.

Filtering of non-linear instabilities. [from finite difference solution of fluid dynamics equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1979-01-01

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Material point method modeling in oil and gas reservoirs

DOEpatents

Vanderheyden, William Brian; Zhang, Duan

2016-06-28

A computer system and method of simulating the behavior of an oil and gas reservoir including changes in the margins of frangible solids. A system of equations including state equations such as momentum, and conservation laws such as mass conservation and volume fraction continuity, are defined and discretized for at least two phases in a modeled volume, one of which corresponds to frangible material. A material point model technique for numerically solving the system of discretized equations, to derive fluid flow at each of a plurality of mesh nodes in the modeled volume, and the velocity of at each of a plurality of particles representing the frangible material in the modeled volume. A time-splitting technique improves the computational efficiency of the simulation while maintaining accuracy on the deformation scale. The method can be applied to derive accurate upscaled model equations for larger volume scale simulations.

Pair correlation function and nonlinear kinetic equation for a spatially uniform polarizable nonideal plasma

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

Belyi, V.V.; Kukharenko, Y.A.; Wallenborn, J.

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. {copyright} {ital 1996 The American Physical Society.}

Magnetic Compression Experiment at General Fusion with Simulation Results

NASA Astrophysics Data System (ADS)

Dunlea, Carl; Khalzov, Ivan; Hirose, Akira; Xiao, Chijin; Fusion Team, General

2017-10-01

The magnetic compression experiment at GF was a repetitive non-destructive test to study plasma physics applicable to Magnetic Target Fusion compression. A spheromak compact torus (CT) is formed with a co-axial gun into a containment region with an hour-glass shaped inner flux conserver, and an insulating outer wall. External coil currents keep the CT off the outer wall (levitation) and then rapidly compress it inwards. The optimal external coil configuration greatly improved both the levitated CT lifetime and the rate of shots with good compressional flux conservation. As confirmed by spectrometer data, the improved levitation field profile reduced plasma impurity levels by suppressing the interaction between plasma and the insulating outer wall during the formation process. We developed an energy and toroidal flux conserving finite element axisymmetric MHD code to study CT formation and compression. The Braginskii MHD equations with anisotropic heat conduction were implemented. To simulate plasma / insulating wall interaction, we couple the vacuum field solution in the insulating region to the full MHD solution in the remainder of the domain. We see good agreement between simulation and experiment results. Partly funded by NSERC and MITACS Accelerate.

Dark optical, singular solitons and conservation laws to the nonlinear Schrödinger’s equation with spatio-temporal dispersion

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-05-01

This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.

Code Development of Three-Dimensional General Relativistic Hydrodynamics with AMR (Adaptive-Mesh Refinement) and Results from Special and General Relativistic Hydrodynamics

NASA Astrophysics Data System (ADS)

Dönmez, Orhan

2004-09-01

In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.

HYDRA-II: A hydrothermal analysis computer code: Volume 2, User's manual

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

McCann, R.A.; Lowery, P.S.; Lessor, D.L.

1987-09-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite-difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equations formore » conservation of momentum incorporate directional porosities and permeabilities that are available to model solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated methods are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume 1 - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. This volume, Volume 2 - User's Manual, contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a sample problem. The final volume, Volume 3 - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. 6 refs.« less

Geophysical aspects of underground fluid dynamics and mineral transformation process

NASA Astrophysics Data System (ADS)

Khramchenkov, Maxim; Khramchenkov, Eduard

2014-05-01

The description of processes of mass exchange between fluid and poly-minerals material in porous media from various kinds of rocks (primarily, sedimentary rocks) have been examined. It was shown that in some important cases there is a storage equation of non-linear diffusion equation type. In addition, process of filtration in un-swelling soils, swelling porous rocks and coupled process of consolidation and chemical interaction between fluid and particles material were considered. In the latter case equations of physical-chemical mechanics of conservation of mass for fluid and particles material were used. As it is well known, the mechanics of porous media is theoretical basis of such branches of science as rock mechanics, soil physics and so on. But at the same moment some complex processes in the geosystems lacks full theoretical description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid components, heat release and absorption, phase transitions, rock destruction occurs. Extensive usage of computational resources in limits of traditional models of the mechanics of porous media cannot guarantee full correctness of obtained models and results. The process of rocks consolidation which happens due to filtration of underground fluids is described from the position of rock mechanics. As an additional impact, let us consider the porous media consolidating under the weight of overlying rock with coupled complex geological processes, as a continuous porous medium of variable mass. Problems of obtaining of correct storage equations for coupled processes of consolidation and mass exchange between underground fluid and skeleton material are often met in catagenesi processes description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid components, heat release and absorption, phase transitions, rock destruction occurs. Extensive usage of computational resources in limits of traditional models of the mechanics of porous media cannot guarantee full correctness of obtained models and results. The present work is dedicated to the retrieval of new ways to formulate and construct such models. It was shown that in some important cases there is a governing equation of non-linear diffusion equation type (well-known Fisher equation). In addition, some geophysical aspects of filtration process in usual non-swelling soils, swelling porous rocks and coupled process of consolidation and chemical interaction between fluid and skeleton material, including earth quakes, are considered.

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

Băloi, Mihaela-Andreea, E-mail: mihaela.baloi88@e-uvt.ro; Crucean, Cosmin

The production of fermions in dipolar electric fields on de Sitter universe is studied. The amplitude and probability of pair production are computed using the exact solution of the Dirac equation in de Sitter spacetime. The form of the dipolar fields is established using the conformal invariance of the Maxwell equations. We obtain that the momentum conservation law is broken in the process of pair production in dipolar electric fields. Also we establish that there are nonvanishing probabilities for processes in which the helicity is conserved/nonconserved. The Minkowski limit is recovered when the expansion factor becomes zero.

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

NASA Technical Reports Server (NTRS)

Nordmann, R.; Weiser, P.

1989-01-01

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

Numerical Limitations of 1D Hydraulic Models Using MIKE11 or HEC-RAS software - Case study of Baraolt River, Romania

NASA Astrophysics Data System (ADS)

Andrei, Armas; Robert, Beilicci; Erika, Beilicci

2017-10-01

MIKE 11 is an advanced hydroinformatic tool, a professional engineering software package for simulation of one-dimensional flows in estuaries, rivers, irrigation systems, channels and other water bodies. MIKE 11 is a 1-dimensional river model. It was developed by DHI Water · Environment · Health, Denmark. The basic computational procedure of HEC-RAS for steady flow is based on the solution of the one-dimensional energy equation. Energy losses are evaluated by friction and contraction / expansion. The momentum equation may be used in situations where the water surface profile is rapidly varied. These situations include hydraulic jumps, hydraulics of bridges, and evaluating profiles at river confluences. For unsteady flow, HEC-RAS solves the full, dynamic, 1-D Saint Venant Equation using an implicit, finite difference method. The unsteady flow equation solver was adapted from Dr. Robert L. Barkau’s UNET package. Fluid motion is controlled by the basic principles of conservation of mass, energy and momentum, which form the basis of fluid mechanics and hydraulic engineering. Complex flow situations must be solved using empirical approximations and numerical models, which are based on derivations of the basic principles (backwater equation, Navier-Stokes equation etc.). All numerical models are required to make some form of approximation to solve these principles, and consequently all have their limitations. The study of hydraulics and fluid mechanics is founded on the three basic principles of conservation of mass, energy and momentum. Real-life situations are frequently too complex to solve without the aid of numerical models. There is a tendency among some engineers to discard the basic principles taught at university and blindly assume that the results produced by the model are correct. Regardless of the complexity of models and despite the claims of their developers, all numerical models are required to make approximations. These may be related to geometric limitations, numerical simplification, or the use of empirical correlations. Some are obvious: one-dimensional models must average properties over the two remaining directions. It is the less obvious and poorly advertised approximations that pose the greatest threat to the novice user. Some of these, such as the inability of one-dimensional unsteady models to simulate supercritical flow can cause significant inaccuracy in the model predictions.

HAM2D: 2D Shearing Box Model

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; Guan, Xiaoyue

2012-10-01

HAM solves non-relativistic hyperbolic partial differential equations in conservative form using high-resolution shock-capturing techniques. This version of HAM has been configured to solve the magnetohydrodynamic equations of motion in axisymmetry to evolve a shearing box model.

Nada: A new code for studying self-gravitating tori around black holes

NASA Astrophysics Data System (ADS)

Montero, Pedro J.; Font, José A.; Shibata, Masaru

2008-09-01

We present a new two-dimensional numerical code called Nada designed to solve the full Einstein equations coupled to the general relativistic hydrodynamics equations. The code is mainly intended for studies of self-gravitating accretion disks (or tori) around black holes, although it is also suitable for regular spacetimes. Concerning technical aspects the Einstein equations are formulated and solved in the code using a formulation of the standard 3+1 Arnowitt-Deser-Misner canonical formalism system, the so-called Baumgarte-Shapiro Shibata-Nakamura approach. A key feature of the code is that derivative terms in the spacetime evolution equations are computed using a fourth-order centered finite difference approximation in conjunction with the Cartoon method to impose the axisymmetry condition under Cartesian coordinates (the choice in Nada), and the puncture/moving puncture approach to carry out black hole evolutions. Correspondingly, the general relativistic hydrodynamics equations are written in flux-conservative form and solved with high-resolution, shock-capturing schemes. We perform and discuss a number of tests to assess the accuracy and expected convergence of the code, namely, (single) black hole evolutions, shock tubes, and evolutions of both spherical and rotating relativistic stars in equilibrium, the gravitational collapse of a spherical relativistic star leading to the formation of a black hole. In addition, paving the way for specific applications of the code, we also present results from fully general relativistic numerical simulations of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium.

A finite-volume Eulerian-Lagrangian Localized Adjoint Method for solution of the advection-dispersion equation

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1993-01-01

A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.

Rolling Bearing Life Prediction-Past, Present, and Future

NASA Technical Reports Server (NTRS)

Zaretsky, E V; Poplawski, J. V.; Miller, C. R.

2000-01-01

Comparisons were made between the life prediction formulas of Lundberg and Palmgren, Ioannides and Harris, and Zaretsky and full-scale ball and roller bearing life data. The effect of Weibull slope on bearing life prediction was determined. Life factors are proposed to adjust the respective life formulas to the normalized statistical life distribution of each bearing type. The Lundberg-Palmgren method resulted in the most conservative life predictions compared to Ioannides and Harris, and Zaretsky methods which produced statistically similar results. Roller profile can have significant effects on bearing life prediction results. Roller edge loading can reduce life by as much as 98 percent. The resultant predicted life not only depends on the life equation used but on the Weibull slope assumed, the least variation occurring with the Zaretsky equation. The load-life exponent p of 10/3 used in the American National Standards Institute (ANSI)/American Bearing Manufacturers Association (ABMA)/International Organization for Standardization (ISO) standards is inconsistent with the majority roller bearings designed and used today.

Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Plank Collision Operator

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2014-06-20

Here, COGENT is a continuum gyrokinetic code for edge plasma simulations being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of a fourth-order finite-volume (conservative) discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. The distribution function F is discretized in v∥ – μ (parallel velocity – magnetic moment) velocity coordinates, and the code presently solves an axisymmetric full-f gyro-kinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. COGENT capabilities are extended by implementing the fully nonlinear Fokker-Plank operator to model Coulomb collisions in magnetized edge plasmas.more » The corresponding Rosenbluth potentials are computed by making use of a finite-difference scheme and multipole-expansion boundary conditions. Details of the numerical algorithms and results of the initial verification studies are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)« less

CAS2D: FORTRAN program for nonrotating blade-to-blade, steady, potential transonic cascade flows

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1980-01-01

An exact, full-potential-equation (FPE) model for the steady, irrotational, homentropic and homoenergetic flow of a compressible, homocompositional, inviscid fluid through two dimensional planar cascades of airfoils was derived, together with its appropriate boundary conditions. A computer program, CAS2D, was developed that numerically solves an artificially time-dependent form of the actual FPE. The governing equation was discretized by using type-dependent, rotated finite differencing and the finite area technique. The flow field was discretized by providing a boundary-fitted, nonuniform computational mesh. The mesh was generated by using a sequence of conforming mapping, nonorthogonal coordinate stretching, and local, isoparametric, bilinear mapping functions. The discretized form of the FPE was solved iteratively by using successive line overrelaxation. The possible isentropic shocks were correctly captured by adding explicitly an artificial viscosity in a conservative form. In addition, a three-level consecutive, mesh refinement feature makes CAS2D a reliable and fast algorithm for the analysis of transonic, two dimensional cascade flows.

Effects of Non-Equilibrium Chemistry and Darcy-Forchheimer Flow of Pyrolysis Gas for a Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2011-01-01

The Fully Implicit Ablation and Thermal Response code, FIAT, simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid. This work describes new modeling capabilities that are added to a special version of FIAT. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite-rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Parametric studies are performed using this enhanced version of FIAT. Two groups of analyses of Phenolic Impregnated Carbon Ablator (PICA) are presented. In the first group, an Orion flight environment for a proposed Lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on PICA material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results are presented, discussed, and compared with those predicted by the baseline PICA/FIAT ablation and thermal response model developed by the Orion Thermal Protection System Advanced Development Project.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics.

PubMed

Aguayo-Ortiz, A; Mendoza, S; Olvera, D

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.

Applying Boundary Conditions Using a Time-Dependent Lagrangian for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, Jonathan; Shadwick, B. A.

2016-10-01

Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics

PubMed Central

Mendoza, S.; Olvera, D.

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and “Rankine-Hugoniot” jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges. PMID:29659602

A conservation law for virus infection kinetics in vitro.

PubMed

Kakizoe, Yusuke; Morita, Satoru; Nakaoka, Shinji; Takeuchi, Yasuhiro; Sato, Kei; Miura, Tomoyuki; Beauchemin, Catherine A A; Iwami, Shingo

2015-07-07

Conservation laws are among the most important properties of a physical system, but are not commonplace in biology. We derived a conservation law from the basic model for viral infections which consists in a small set of ordinary differential equations. We challenged the conservation law experimentally for the case of a virus infection in a cell culture. We found that the derived, conserved quantity remained almost constant throughout the infection period, implying that the derived conservation law holds in this biological system. We also suggest a potential use for the conservation law in evaluating the accuracy of experimental measurements. Copyright © 2015 Elsevier Ltd. All rights reserved.

Distributed Relaxation for Conservative Discretizations

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2001-01-01

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Mesoscale Modeling of LX-17 Under Isentropic Compression

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

Springer, H K; Willey, T M; Friedman, G

Mesoscale simulations of LX-17 incorporating different equilibrium mixture models were used to investigate the unreacted equation-of-state (UEOS) of TATB. Candidate TATB UEOS were calculated using the equilibrium mixture models and benchmarked with mesoscale simulations of isentropic compression experiments (ICE). X-ray computed tomography (XRCT) data provided the basis for initializing the simulations with realistic microstructural details. Three equilibrium mixture models were used in this study. The single constituent with conservation equations (SCCE) model was based on a mass-fraction weighted specific volume and the conservation of mass, momentum, and energy. The single constituent equation-of-state (SCEOS) model was based on a mass-fraction weightedmore » specific volume and the equation-of-state of the constituents. The kinetic energy averaging (KEA) model was based on a mass-fraction weighted particle velocity mixture rule and the conservation equations. The SCEOS model yielded the stiffest TATB EOS (0.121{micro} + 0.4958{micro}{sup 2} + 2.0473{micro}{sup 3}) and, when incorporated in mesoscale simulations of the ICE, demonstrated the best agreement with VISAR velocity data for both specimen thicknesses. The SCCE model yielded a relatively more compliant EOS (0.1999{micro}-0.6967{micro}{sup 2} + 4.9546{micro}{sup 3}) and the KEA model yielded the most compliant EOS (0.1999{micro}-0.6967{micro}{sup 2}+4.9546{micro}{sup 3}) of all the equilibrium mixture models. Mesoscale simulations with the lower density TATB adiabatic EOS data demonstrated the least agreement with VISAR velocity data.« less

Lie-Mei symmetry and conserved quantities of the Rosenberg problem

NASA Astrophysics Data System (ADS)

Liu, Xiao-Wei; Li, Yuan-Cheng

2011-07-01

The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry.

Numerical Modeling of Conjugate Heat Transfer in Fluid Network

NASA Technical Reports Server (NTRS)

Majumdar, Alok

2004-01-01

Fluid network modeling with conjugate heat transfer has many applications in Aerospace engineering. In modeling unsteady flow with heat transfer, it is important to know the variation of wall temperature in time and space to calculate heat transfer between solid to fluid. Since wall temperature is a function of flow, a coupled analysis of temperature of solid and fluid is necessary. In cryogenic applications, modeling of conjugate heat transfer is of great importance to correctly predict boil-off rate in propellant tanks and chill down of transfer lines. In TFAWS 2003, the present author delivered a paper to describe a general-purpose computer program, GFSSP (Generalized Fluid System Simulation Program). GFSSP calculates flow distribution in complex flow circuit for compressible/incompressible, with or without heat transfer or phase change in all real fluids or mixtures. The flow circuit constitutes of fluid nodes and branches. The mass, energy and specie conservation equations are solved at the nodes where as momentum conservation equations are solved at the branches. The proposed paper describes the extension of GFSSP to model conjugate heat transfer. The network also includes solid nodes and conductors in addition to fluid nodes and branches. The energy conservation equations for solid nodes solves to determine the temperatures of the solid nodes simultaneously with all conservation equations governing fluid flow. The numerical scheme accounts for conduction, convection and radiation heat transfer. The paper will also describe the applications of the code to predict chill down of cryogenic transfer line and boil-off rate of cryogenic propellant storage tank.

Wave equations on anti self dual (ASD) manifolds

NASA Astrophysics Data System (ADS)

Bashingwa, Jean-Juste; Kara, A. H.

2017-11-01

In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

Einstein's osmotic equilibrium of colloidal suspensions in conservative force fields

NASA Astrophysics Data System (ADS)

Fu, Jinxin; Ou-Yang, H. Daniel

2014-09-01

Predicted by Einstein in his 1905 paper on Brownian motion, colloidal particles in suspension reach osmotic equilibrium under gravity. The idea was demonstrated by J.B. Perrin to win Nobel Prize in Physics in 1926. We show Einstein's equation for osmotic equilibrium can be applied to colloids in a conservative force field generated by optical gradient forces. We measure the osmotic equation of state of 100nm Polystyrene latex particles in the presence of KCl salt and PEG polymer. We also obtain the osmotic compressibility, which is important for determining colloidal stability and the internal chemical potential, which is useful for predicting the phase transition of colloidal systems. This generalization allows for the use of any conservative force fields for systems ranging from colloidal systems to macromolecular solutions.

Lectures series in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Thompson, Kevin W.

1987-01-01

The lecture notes cover the basic principles of computational fluid dynamics (CFD). They are oriented more toward practical applications than theory, and are intended to serve as a unified source for basic material in the CFD field as well as an introduction to more specialized topics in artificial viscosity and boundary conditions. Each chapter in the test is associated with a videotaped lecture. The basic properties of conservation laws, wave equations, and shock waves are described. The duality of the conservation law and wave representations is investigated, and shock waves are examined in some detail. Finite difference techniques are introduced for the solution of wave equations and conservation laws. Stability analysis for finite difference approximations are presented. A consistent description of artificial viscosity methods are provided. Finally, the problem of nonreflecting boundary conditions are treated.

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

NASA Astrophysics Data System (ADS)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

Method and Apparatus for Predicting Unsteady Pressure and Flow Rate Distribution in a Fluid Network

NASA Technical Reports Server (NTRS)

Majumdar, Alok K. (Inventor)

2009-01-01

A method and apparatus for analyzing steady state and transient flow in a complex fluid network, modeling phase changes, compressibility, mixture thermodynamics, external body forces such as gravity and centrifugal force and conjugate heat transfer. In some embodiments, a graphical user interface provides for the interactive development of a fluid network simulation having nodes and branches. In some embodiments, mass, energy, and specific conservation equations are solved at the nodes, and momentum conservation equations are solved in the branches. In some embodiments, contained herein are data objects for computing thermodynamic and thermophysical properties for fluids. In some embodiments, the systems of equations describing the fluid network are solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods.

Numerical investigation of shock induced bubble collapse in water

NASA Astrophysics Data System (ADS)

Apazidis, N.

2016-04-01

A semi-conservative, stable, interphase-capturing numerical scheme for shock propagation in heterogeneous systems is applied to the problem of shock propagation in liquid-gas systems. The scheme is based on the volume-fraction formulation of the equations of motion for liquid and gas phases with separate equations of state. The semi-conservative formulation of the governing equations ensures the absence of spurious pressure oscillations at the material interphases between liquid and gas. Interaction of a planar shock in water with a single spherical bubble as well as twin adjacent bubbles is investigated. Several stages of the interaction process are considered, including focusing of the transmitted shock within the deformed bubble, creation of a water-hammer shock as well as generation of high-speed liquid jet in the later stages of the process.

Initial verification and validation of RAZORBACK - A research reactor transient analysis code

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

Talley, Darren G.

2015-09-01

This report describes the work and results of the initial verification and validation (V&V) of the beta release of the Razorback code. Razorback is a computer code designed to simulate the operation of a research reactor (such as the Annular Core Research Reactor (ACRR)) by a coupled numerical solution of the point reactor kinetics equations, the energy conservation equation for fuel element heat transfer, and the mass, momentum, and energy conservation equations for the water cooling of the fuel elements. This initial V&V effort was intended to confirm that the code work to-date shows good agreement between simulation and actualmore » ACRR operations, indicating that the subsequent V&V effort for the official release of the code will be successful.« less

An Entropy-Based Approach to Nonlinear Stability

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Brownian microhydrodynamics of active filaments.

PubMed

Laskar, Abhrajit; Adhikari, R

2015-12-21

Slender bodies capable of spontaneous motion in the absence of external actuation in an otherwise quiescent fluid are common in biological, physical and technological contexts. The interplay between the spontaneous fluid flow, Brownian motion, and the elasticity of the body presents a challenging fluid-structure interaction problem. Here, we model this problem by approximating the slender body as an elastic filament that can impose non-equilibrium velocities or stresses at the fluid-structure interface. We derive equations of motion for such an active filament by enforcing momentum conservation in the fluid-structure interaction and assuming slow viscous flow in the fluid. The fluid-structure interaction is obtained, to any desired degree of accuracy, through the solution of an integral equation. A simplified form of the equations of motion, which allows for efficient numerical solutions, is obtained by applying the Kirkwood-Riseman superposition approximation to the integral equation. We use this form of equation of motion to study dynamical steady states in free and hinged minimally active filaments. Our model provides the foundation to study collective phenomena in momentum-conserving, Brownian, active filament suspensions.

On the global well-posedness of BV weak solutions to the Kuramoto-Sakaguchi equation

NASA Astrophysics Data System (ADS)

Amadori, Debora; Ha, Seung-Yeal; Park, Jinyeong

2017-01-01

The Kuramoto model is a prototype phase model describing the synchronous behavior of weakly coupled limit-cycle oscillators. When the number of oscillators is sufficiently large, the dynamics of Kuramoto ensemble can be effectively approximated by the corresponding mean-field equation, namely "the Kuramoto-Sakaguchi (KS) equation". This KS equation is a kind of scalar conservation law with a nonlocal flux function due to the mean-field interactions among oscillators. In this paper, we provide a unique global solvability of bounded variation (BV) weak solutions to the kinetic KS equation for identical oscillators using the method of front-tracking in hyperbolic conservation laws. Moreover, we also show that our BV weak solutions satisfy local-in-time L1-stability with respect to BV-initial data. For the ensemble of identical Kuramoto oscillators, we explicitly construct an exponentially growing BV weak solution generated from BV perturbation of incoherent state for any positive coupling strength. This implies the nonlinear instability of incoherent state in a positive coupling strength regime. We provide several numerical examples and compare them with our analytical results.

A conservative, thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration

NASA Astrophysics Data System (ADS)

Nonaka, Andrew; Day, Marcus S.; Bell, John B.

2018-01-01

We present a numerical approach for low Mach number combustion that conserves both mass and energy while remaining on the equation of state to a desired tolerance. We present both unconfined and confined cases, where in the latter the ambient pressure changes over time. Our overall scheme is a projection method for the velocity coupled to a multi-implicit spectral deferred corrections (SDC) approach to integrate the mass and energy equations. The iterative nature of SDC methods allows us to incorporate a series of pressure discrepancy corrections naturally that lead to additional mass and energy influx/outflux in each finite volume cell in order to satisfy the equation of state. The method is second order, and satisfies the equation of state to a desired tolerance with increasing iterations. Motivated by experimental results, we test our algorithm on hydrogen flames with detailed kinetics. We examine the morphology of thermodiffusively unstable cylindrical premixed flames in high-pressure environments for confined and unconfined cases. We also demonstrate that our algorithm maintains the equation of state for premixed methane flames and non-premixed dimethyl ether jet flames.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-07-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+-up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-03-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+ -up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

Mathematical modeling of impact of two metal plates using two-fluid approach

NASA Astrophysics Data System (ADS)

Utkin, P. S.; Fortova, S. V.

2018-01-01

The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

NASA Technical Reports Server (NTRS)

Larson, V. H.

1982-01-01

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.

Alfvén wave interactions in the solar wind

NASA Astrophysics Data System (ADS)

Webb, G. M.; McKenzie, J. F.; Hu, Q.; le Roux, J. A.; Zank, G. P.

2012-11-01

Alfvén wave mixing (interaction) equations used in locally incompressible turbulence transport equations in the solar wind are analyzed from the perspective of linear wave theory. The connection between the wave mixing equations and non-WKB Alfven wave driven wind theories are delineated. We discuss the physical wave energy equation and the canonical wave energy equation for non-WKB Alfven waves and the WKB limit. Variational principles and conservation laws for the linear wave mixing equations for the Heinemann and Olbert non-WKB wind model are obtained. The connection with wave mixing equations used in locally incompressible turbulence transport in the solar wind are discussed.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Use of transport models for wildfire behavior simulations

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

Linn, R.R.; Harlow, F.H.

1998-01-01

Investigators have attempted to describe the behavior of wildfires for over fifty years. Current models for numerical description are mainly algebraic and based on statistical or empirical ideas. The authors have developed a transport model called FIRETEC. The use of transport formulations connects the propagation rates to the full conservation equations for energy, momentum, species concentrations, mass, and turbulence. In this paper, highlights of the model formulation and results are described. The goal of the FIRETEC model is to describe most probable average behavior of wildfires in a wide variety of conditions. FIRETEC represents the essence of the combination ofmore » many small-scale processes without resolving each process in complete detail.« less

Ice Accretion Modeling using an Eulerian Approach for Droplet Impingement

NASA Technical Reports Server (NTRS)

Kim, Joe Woong; Garza, Dennis P.; Sankar, Lakshmi N.; Kreeger, Richard E.

2012-01-01

A three-dimensional Eulerian analysis has been developed for modeling droplet impingement on lifting bodes. The Eulerian model solves the conservation equations of mass and momentum to obtain the droplet flow field properties on the same mesh used in CFD simulations. For complex configurations such as a full rotorcraft, the Eulerian approach is more efficient because the Lagrangian approach would require a significant amount of seeding for accurate estimates of collection efficiency. Simulations are done for various benchmark cases such as NACA0012 airfoil, MS317 airfoil and oscillating SC2110 airfoil to illustrate its use. The present results are compared with results from the Lagrangian approach used in an industry standard analysis called LEWICE.

Fourth-Order Conservative Vlasov-Maxwell Solver for Cartesian and Cylindrical Phase Space Coordinates

NASA Astrophysics Data System (ADS)

Vogman, Genia

Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space coordinates present a new development in the field of computational plasma physics. A fourth-order finite-volume method for solving the Vlasov-Maxwell equation system is presented first for Cartesian and then for cylindrical phase space coordinates. Special attention is given to the treatment of the discrete primary variables and to the quadrature rule for evaluating the surface and line integrals that appear in the governing equations. The finite-volume treatment of conducting wall and axis boundaries is particularly nuanced when it comes to phase space coordinates, and is described in detail. In addition to the mechanics of each part of the finite-volume discretization in the two different coordinate systems, the complete algorithm is also presented. The Cartesian coordinate discretization is applied to several well-known test problems. Since even linear analysis of kinetic theory governing equations is complicated on account of velocity being an independent coordinate, few analytic or semi-analytic predictions exist. Benchmarks are particularly scarce for configurations that have magnetic fields and involve more than two phase space dimensions. Ensuring that simulations are true to the physics thus presents a difficulty in the development of robust numerical methods. The research described in this dissertation addresses this challenge through the development of more complete physics-based benchmarks based on the Dory-Guest-Harris instability. The instability is a special case of perpendicularly-propagating kinetic electrostatic waves in a warm uniformly magnetized plasma. A complete derivation of the closed-form linear theory dispersion relation for the instability is presented. The electric field growth rates and oscillation frequencies specified by the dispersion relation provide concrete measures against which simulation results can be quantitatively compared. Furthermore, a specialized form of perturbation is shown to strongly excite the fastest growing mode. The fourth-order finite-volume algorithm is benchmarked against the instability, and is demonstrated to have good convergence properties and close agreement with theoretical growth rate and oscillation frequency predictions. The Dory-Guest-Harris instability benchmark extends the scope of standard test problems by providing a substantive means of validating continuum kinetic simulations of warm magnetized plasmas in higher-dimensional 3D ( x,vx,vy) phase space. The linear theory analysis, initial conditions, algorithm description, and comparisons between theoretical predictions and simulation results are presented. The cylindrical coordinate finite-volume discretization is applied to model axisymmetric systems. Since mitigating the prohibitive computational cost of simulating six dimensions is another challenge in phase space simulations, the development of a robust means of exploiting symmetry is a major advance when it comes to numerically solving the Vlasov-Maxwell equation system. The discretization is applied to a uniform distribution function to assess the nature of the singularity at the axis, and is demonstrated to converge at fourth-order accuracy. The numerical method is then applied to simulate electrostatic ion confinement in an axisymmetric Z-pinch configuration. To the author's knowledge this presents the first instance of a conservative finite-volume discretization of the cylindrical coordinate Vlasov equation. The computational framework for the Vlasov-Maxwell solver is described, and an outlook for future research is presented.

A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2014-10-01

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with stiff relaxation source terms.

Initialization and assimilation of cloud and rainwater in a regional model

NASA Technical Reports Server (NTRS)

Raymond, William H.; Olson, William S.

1990-01-01

The initialization and assimilation of cloud and rainwater quantities in a mesoscale regional model was examined. Forecasts of explicit cloud and rainwater are made using conservation equations. The physical processes include condensation, evaporation, autoconversion, accretion, and the removal of rainwater by fallout. These physical processes, some of which are parameterized, represent source and sink in terms in the conservation equations. The question of how to initialize the explicit liquid water calculations in numerical models and how to retain information about precipitation processes during the 4-D assimilation cycle are important issues that are addressed.

Symmetrization of conservation laws with entropy for high-temperature hypersonic computations

NASA Technical Reports Server (NTRS)

Chalot, F.; Hughes, T. J. R.; Shakib, F.

1990-01-01

Results of Hughes, France, and Mallet are generalized to conservation law systems taking into account high-temperature effects. Symmetric forms of different equation sets are derived in terms of entropy variables. First, the case of a general divariant gas is studied; it can be specialized to the usual Navier-Stokes equations, as well as to situations where the gas is vibrationally excited, and undergoes equilibrium chemical reactions. The case of gas in thermochemical nonequilibrium is considered next. Transport phenomena, and in particular mass diffusion, are examined in the framework of symmetric advective-diffusive systems.

TAIR- TRANSONIC AIRFOIL ANALYSIS COMPUTER CODE

NASA Technical Reports Server (NTRS)

Dougherty, F. C.

1994-01-01

The Transonic Airfoil analysis computer code, TAIR, was developed to employ a fast, fully implicit algorithm to solve the conservative full-potential equation for the steady transonic flow field about an arbitrary airfoil immersed in a subsonic free stream. The full-potential formulation is considered exact under the assumptions of irrotational, isentropic, and inviscid flow. These assumptions are valid for a wide range of practical transonic flows typical of modern aircraft cruise conditions. The primary features of TAIR include: a new fully implicit iteration scheme which is typically many times faster than classical successive line overrelaxation algorithms; a new, reliable artifical density spatial differencing scheme treating the conservative form of the full-potential equation; and a numerical mapping procedure capable of generating curvilinear, body-fitted finite-difference grids about arbitrary airfoil geometries. Three aspects emphasized during the development of the TAIR code were reliability, simplicity, and speed. The reliability of TAIR comes from two sources: the new algorithm employed and the implementation of effective convergence monitoring logic. TAIR achieves ease of use by employing a "default mode" that greatly simplifies code operation, especially by inexperienced users, and many useful options including: several airfoil-geometry input options, flexible user controls over program output, and a multiple solution capability. The speed of the TAIR code is attributed to the new algorithm and the manner in which it has been implemented. Input to the TAIR program consists of airfoil coordinates, aerodynamic and flow-field convergence parameters, and geometric and grid convergence parameters. The airfoil coordinates for many airfoil shapes can be generated in TAIR from just a few input parameters. Most of the other input parameters have default values which allow the user to run an analysis in the default mode by specifing only a few input parameters. Output from TAIR may include aerodynamic coefficients, the airfoil surface solution, convergence histories, and printer plots of Mach number and density contour maps. The TAIR program is written in FORTRAN IV for batch execution and has been implemented on a CDC 7600 computer with a central memory requirement of approximately 155K (octal) of 60 bit words. The TAIR program was developed in 1981.

An approximation of herd effect due to vaccinating children against seasonal influenza - a potential solution to the incorporation of indirect effects into static models.

PubMed

Van Vlaenderen, Ilse; Van Bellinghen, Laure-Anne; Meier, Genevieve; Nautrup, Barbara Poulsen

2013-01-22

Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination. Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals. The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation. This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses.

Some new solutions for the Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Ramírez, J.; Romero, J. L.; Tracinà, R.

2013-09-01

The well-known Derrida-Lebowitz-Speer-Spohn equation is investigated. By using specific ansätze and the classical symmetries of the equation, several families of new exact solutions have been found. In particular, there appear traveling waves that include compactons and soliton-compactons. Some other solutions conserve the mass and exhibit diffusion and convection processes from an instantaneous source and localized peakons.

Numerical Solution for Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Warsi, Z. U. A.; Weed, R. A.; Thompson, J. F.

1982-01-01

Carefully selected blend of computational techniques solves complete set of equations for viscous, unsteady, hypersonic flow in general curvilinear coordinates. New algorithm has tested computation of axially directed flow about blunt body having shape similar to that of such practical bodies as wide-body aircraft or artillery shells. Method offers significant computational advantages because of conservation-law form of equations and because it reduces amount of metric data required.

The ion-acoustic soliton: A gas-dynamic viewpoint

NASA Astrophysics Data System (ADS)

McKenzie, J. F.

2002-03-01

The properties of fully nonlinear ion-acoustic solitons are investigated by interpreting conservation of total momentum as the structure equation for the proton flow in the wave. In most studies momentum conservation is regarded as the first integral of the Poisson equation for the electric potential and is interpreted as being analogous to a particle moving in a pseudo-potential well. By adopting an essentially gas-dynamic viewpoint, which emphasizes momentum conservation and the properties of the Bernoulli-type energy equations, the crucial role played by the proton sonic point becomes apparent. The relationship (implied by energy conservation) between the electron and proton speeds in the transition yields a locus—the hodograph of the system-which shows that, in the first half of the soliton, the electrons initially lag behind the protons until the charge neutral point is reached, after which they run ahead of the protons. The system reaches an equilibrium point (the center of the soliton) before the proton flow goes sonic. It follows that the critical ion-acoustic Mach number, Mc, above which smooth, continuous solitons cannot be constructed, stems from the requirement that the two equilibrium points of the structure equation coalesce at the proton sonic point of the flow. In general the range of the ion-acoustic Mach numbers, Mep, in which solitons exist, is extended beyond the classical range 1

A geometric viewpoint on generalized hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Spohn, Herbert; Yoshimura, Takato

2018-01-01

Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective ("dressed") velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.

The turbulent mean-flow, Reynolds-stress, and heat flux equations in mass-averaged dependent variables

NASA Technical Reports Server (NTRS)

Rubesin, M. W.; Rose, W. C.

1973-01-01

The time-dependent, turbulent mean-flow, Reynolds stress, and heat flux equations in mass-averaged dependent variables are presented. These equations are given in conservative form for both generalized orthogonal and axisymmetric coordinates. For the case of small viscosity and thermal conductivity fluctuations, these equations are considerably simpler than the general Reynolds system of dependent variables for a compressible fluid and permit a more direct extension of low speed turbulence modeling to computer codes describing high speed turbulence fields.

7 CFR 610.14 - Use of USLE, RUSLE, and WEQ.

Code of Federal Regulations, 2011 CFR

2011-01-01

..., DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations..., this includes the soil loss tolerance values used in those formulas for determining HEL. The soil loss tolerance value is used as one of the criteria for planning soil conservation systems. These values are...

7 CFR 610.11 - Purpose and scope.

Code of Federal Regulations, 2012 CFR

2012-01-01

... AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.11 Purpose... by the Natural Resources Conservation Service (NRCS) to predict soil erosion due to water and wind... Act, as amended, 16 U.S.C. 3801-3813 specified that the Secretary would publish the universal soil...

7 CFR 610.14 - Use of USLE, RUSLE, and WEQ.

Code of Federal Regulations, 2013 CFR

2013-01-01

..., DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations..., this includes the soil loss tolerance values used in those formulas for determining HEL. The soil loss tolerance value is used as one of the criteria for planning soil conservation systems. These values are...

7 CFR 610.11 - Purpose and scope.

Code of Federal Regulations, 2013 CFR

2013-01-01

... AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.11 Purpose... by the Natural Resources Conservation Service (NRCS) to predict soil erosion due to water and wind... Act, as amended, 16 U.S.C. 3801-3813 specified that the Secretary would publish the universal soil...

7 CFR 610.11 - Purpose and scope.

Code of Federal Regulations, 2010 CFR

2010-01-01

... AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.11 Purpose... by the Natural Resources Conservation Service (NRCS) to predict soil erosion due to water and wind... Act, as amended, 16 U.S.C. 3801-3813 specified that the Secretary would publish the universal soil...

7 CFR 610.14 - Use of USLE, RUSLE, and WEQ.

Code of Federal Regulations, 2014 CFR

2014-01-01

..., DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations..., this includes the soil loss tolerance values used in those formulas for determining HEL. The soil loss tolerance value is used as one of the criteria for planning soil conservation systems. These values are...

7 CFR 610.11 - Purpose and scope.

Code of Federal Regulations, 2011 CFR

2011-01-01

... AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.11 Purpose... by the Natural Resources Conservation Service (NRCS) to predict soil erosion due to water and wind... Act, as amended, 16 U.S.C. 3801-3813 specified that the Secretary would publish the universal soil...

7 CFR 610.14 - Use of USLE, RUSLE, and WEQ.

Code of Federal Regulations, 2012 CFR

2012-01-01

..., DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations..., this includes the soil loss tolerance values used in those formulas for determining HEL. The soil loss tolerance value is used as one of the criteria for planning soil conservation systems. These values are...

7 CFR 610.14 - Use of USLE, RUSLE, and WEQ.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., DEPARTMENT OF AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations..., this includes the soil loss tolerance values used in those formulas for determining HEL. The soil loss tolerance value is used as one of the criteria for planning soil conservation systems. These values are...

7 CFR 610.11 - Purpose and scope.

Code of Federal Regulations, 2014 CFR

2014-01-01

... AGRICULTURE CONSERVATION OPERATIONS TECHNICAL ASSISTANCE Soil Erosion Prediction Equations § 610.11 Purpose... by the Natural Resources Conservation Service (NRCS) to predict soil erosion due to water and wind... Act, as amended, 16 U.S.C. 3801-3813 specified that the Secretary would publish the universal soil...

Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory

DOE PAGES

Mendl, Christian B.; Lu, Jianfeng; Lukkarinen, Jani

2016-12-02

We perform microscopic molecular dynamics simulations of particle chains with an onsite anharmonicity to study relaxation of spatially homogeneous states to equilibrium, and directly compare the simulations with the corresponding Boltzmann-Peierls kinetic theory. The Wigner function serves as a common interface between the microscopic and kinetic level. We demonstrate quantitative agreement after an initial transient time interval. In particular, besides energy conservation, we observe the additional quasiconservation of the phonon density, defined via an ensemble average of the related microscopic field variables and exactly conserved by the kinetic equations. On superkinetic time scales, density quasiconservation is lost while energy remainsmore » conserved, and we find evidence for eventual relaxation of the density to its canonical ensemble value. Furthermore, the precise mechanism remains unknown and is not captured by the Boltzmann-Peierls equations.« less

Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory

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

Mendl, Christian B.; Lu, Jianfeng; Lukkarinen, Jani

We perform microscopic molecular dynamics simulations of particle chains with an onsite anharmonicity to study relaxation of spatially homogeneous states to equilibrium, and directly compare the simulations with the corresponding Boltzmann-Peierls kinetic theory. The Wigner function serves as a common interface between the microscopic and kinetic level. We demonstrate quantitative agreement after an initial transient time interval. In particular, besides energy conservation, we observe the additional quasiconservation of the phonon density, defined via an ensemble average of the related microscopic field variables and exactly conserved by the kinetic equations. On superkinetic time scales, density quasiconservation is lost while energy remainsmore » conserved, and we find evidence for eventual relaxation of the density to its canonical ensemble value. Furthermore, the precise mechanism remains unknown and is not captured by the Boltzmann-Peierls equations.« less

Theoretical analysis of multiphase flow during oil-well drilling by a conservative model

NASA Astrophysics Data System (ADS)

Nicolas-Lopez, Ruben

2005-11-01

In order to decrease cost and improve drilling operations is necessary a better understood of the flow mechanisms. Therefore, it was carried out a multiphase conservative model that includes three mass equations and a momentum equation. Also, the measured geothermal gradient is utilized by state equations for estimating physical properties of the phases flowing. The mathematical model is solved by numerical conservative schemes. It is used to analyze the interaction among solid-liquid-gas phases. The circulating system consists as follow, the circulating fluid is pumped downward into the drilling pipe until the bottom of the open hole then it flows through the drill bit, and at this point formation cuttings are incorporated to the circulating fluid and carried upward to the surface. The mixture returns up to the surface by an annular flow area. The real operational conditions are fed to conservative model and the results are matched up to field measurements in several oil wells. Mainly, flow rates, drilling rate, well and tool geometries are data to estimate the profiles of pressure, mixture density, equivalent circulating density, gas fraction and solid carrying capacity. Even though the problem is very complex, the model describes, properly, the hydrodynamics of drilling techniques applied at oil fields. *Authors want to thank to Instituto Mexicano del Petroleo and Petroleos Mexicanos for supporting this research.

Deformed coset models from gauged WZW actions

NASA Astrophysics Data System (ADS)

Park, Q.-Han

1994-06-01

A general Lagrangian formulation of integrably deformed G/H-coset models is given. We consider the G/H-coset model in terms of the gauged Wess-Zumino-Witten action and obtain an integrable deformation by adding a potential energy term Tr(gTg -1overlineT) , where algebra elements T, overlineT belong to the center of the algebra h associated with the subgroup H. We show that the classical equation of motion of the deformed coset model can be identified with the integrability condition of certain linear equations which makes the use of the inverse scattering method possible. Using the linear equation, we give a systematic way to construct infinitely many conserved currents as well as soliton solutions. In the case of the parafermionic SU(2)/U(1)-coset model, we derive n-solitons and conserved currents explicitly.

Unified Framework for Deriving Simultaneous Equation Algorithms for Water Distribution Networks

EPA Science Inventory

The known formulations for steady state hydraulics within looped water distribution networks are re-derived in terms of linear and non-linear transformations of the original set of partly linear and partly non-linear equations that express conservation of mass and energy. All of ...

On the optimal systems of subalgebras for the equations of hydrodynamic stability analysis of smooth shear flows and their group-invariant solutions

NASA Astrophysics Data System (ADS)

Hau, Jan-Niklas; Oberlack, Martin; Chagelishvili, George

2017-04-01

We present a unifying solution framework for the linearized compressible equations for two-dimensional linearly sheared unbounded flows using the Lie symmetry analysis. The full set of symmetries that are admitted by the underlying system of equations is employed to systematically derive the one- and two-dimensional optimal systems of subalgebras, whose connected group reductions lead to three distinct invariant ansatz functions for the governing sets of partial differential equations (PDEs). The purpose of this analysis is threefold and explicitly we show that (i) there are three invariant solutions that stem from the optimal system. These include a general ansatz function with two free parameters, as well as the ansatz functions of the Kelvin mode and the modal approach. Specifically, the first approach unifies these well-known ansatz functions. By considering two limiting cases of the free parameters and related algebraic transformations, the general ansatz function is reduced to either of them. This fact also proves the existence of a link between the Kelvin mode and modal ansatz functions, as these appear to be the limiting cases of the general one. (ii) The Lie algebra associated with the Lie group admitted by the PDEs governing the compressible dynamics is a subalgebra associated with the group admitted by the equations governing the incompressible dynamics, which allows an additional (scaling) symmetry. Hence, any consequences drawn from the compressible case equally hold for the incompressible counterpart. (iii) In any of the systems of ordinary differential equations, derived by the three ansatz functions in the compressible case, the linearized potential vorticity is a conserved quantity that allows us to analyze vortex and wave mode perturbations separately.

Dynamically Consistent Shallow-Atmosphere Equations with a Complete Coriolis force

NASA Astrophysics Data System (ADS)

Tort, Marine; Dubos, Thomas; Bouchut, François; Zeitlin, Vladimir

2014-05-01

Dynamically Consistent Shallow-Atmosphere Equations with a Complete Coriolis force Marine Tort1, Thomas Dubos1, François Bouchut2 & Vladimir Zeitlin1,3 1 Laboratoire of Dynamical Meteorology, Univ. P. and M. Curie, Ecole Normale Supérieure, and Ecole Polytechnique, FRANCE 2 Université Paris-Est, Laboratoire d'Analyse et de Mathématiques Appliquées, FRANCE 3 Institut Universitaire de France Atmospheric and oceanic motion are usually modeled within the shallow-fluid approximation, which simplifies the 3D spherical geometry. For dynamical consistency, i.e. to ensure conservation laws for potential vorticity, energy and angular momentum, the horizontal component of the Coriolis force is neglected. Here new equation sets combining consistently a simplified shallow-fluid geometry with a complete Coriolis force is presented. The derivation invokes Hamilton's principle of least action with an approximate Lagrangian capturing the small increase with height of the solid-body entrainment velocity due to planetary rotation. A three-dimensional compressible model and a one-layer shallow-water model are obtained. The latter extends previous work done on the f-plane and β-plane. Preliminary numerical results confirm the accuracy of the 3D model within the range of parameters for which the equations are relevant. These new models could be useful to incorporate a full Coriolis force into existing numerical models and to disentangle the effects of the shallow-atmosphere approximation from those of the traditional approximation. Related papers: Tort M., Dubos T., Bouchut F. and Zeitlin V. Consistent shallow-water equations on the rotating sphere with complete Coriolis force and topography. J. Fluid Mech. (under revisions) Tort M. and Dubos T. Dynamically consistent shallow-atmosphere equations with a complete Coriolis force. Q.J.R. Meteorol. Soc. (DOI: 10.1002/qj.2274)

Utility of Equations to Estimate Peak Oxygen Uptake and Work Rate From a 6-Minute Walk Test in Patients With COPD in a Clinical Setting.

PubMed

Kirkham, Amy A; Pauhl, Katherine E; Elliott, Robyn M; Scott, Jen A; Doria, Silvana C; Davidson, Hanan K; Neil-Sztramko, Sarah E; Campbell, Kristin L; Camp, Pat G

2015-01-01

To determine the utility of equations that use the 6-minute walk test (6MWT) results to estimate peak oxygen uptake ((Equation is included in full-text article.)o2) and peak work rate with chronic obstructive pulmonary disease (COPD) patients in a clinical setting. This study included a systematic review to identify published equations estimating peak (Equation is included in full-text article.)o2 and peak work rate in watts in COPD patients and a retrospective chart review of data from a hospital-based pulmonary rehabilitation program. The following variables were abstracted from the records of 42 consecutively enrolled COPD patients: measured peak (Equation is included in full-text article.)o2 and peak work rate achieved during a cycle ergometer cardiopulmonary exercise test, 6MWT distance, age, sex, weight, height, forced expiratory volume in 1 second, forced vital capacity, and lung diffusion capacity. Estimated peak (Equation is included in full-text article.)o2 and peak work rate were estimated from 6MWT distance using published equations. The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work to prescribe aerobic exercise intensities of 60% and 80% was calculated. Eleven equations from 6 studies were identified. Agreement between estimated and measured values was poor to moderate (intraclass correlation coefficients = 0.11-0.63). The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work rate to prescribe exercise intensities of 60% and 80% of measured values ranged from mean differences of 12 to 35 and 16 to 47 percentage points, respectively. There is poor to moderate agreement between measured peak (Equation is included in full-text article.)o2 and peak work rate and estimations from equations that use 6MWT distance, and the use of the estimated values for prescription of aerobic exercise intensity would result in large error. Equations estimating peak (Equation is included in full-text article.)o2 and peak work rate are of low utility for prescribing exercise intensity in pulmonary rehabilitation programs.

An Examination of Growing Trends in Land Tenure and Conservation Practice Adoption: Results from a Farmer Survey in Iowa.

PubMed

Varble, Sarah; Secchi, Silvia; Druschke, Caroline Gottschalk

2016-02-01

Tenants and part-owners are farming an increasing number of acres in the United States, while full-owners are farming fewer acres. This shift in ownership is a potential cause for concern because some previous research indicated that tenant and part-owner farmers were less likely to adopt conservation practices than farmers who owned the land they farmed. If that trend persists, ownership changes would signal a national drop in conservation adoption. Here we examine this issue using a survey of agricultural operators in the Clear Creek watershed in Iowa, a state with intensive agricultural production. We compare adoption of conservation practices, and preferences for conservation information sources and communication channels, between farmers who rent some portion of the land they farm (tenants and part-owners) and farmers who own all of the land they farm (full-owners). We find that renters are more likely to practice conservation tillage than full-owners, though they are less likely to rotate crops. In addition, renters report using federal government employees (specifically, Natural Resource Conservation Service and Farm Service Agency) as their primary sources of conservation information, while full-owners most frequently rely on neighbors, friends, and County Extension. These findings are significant for conservation policy because, unlike some past research, they indicate that renters are not resistant to all types of conservation practices, echoing recent studies finding an increase in conservation adoption among non-full-owners. Our results emphasize the importance of government conservation communication and can inform outreach efforts by helping tailor effective, targeted conservation strategies for owners and renters.

An Examination of Growing Trends in Land Tenure and Conservation Practice Adoption: Results from a Farmer Survey in Iowa

NASA Astrophysics Data System (ADS)

Varble, Sarah; Secchi, Silvia; Druschke, Caroline Gottschalk

2016-02-01

Tenants and part-owners are farming an increasing number of acres in the United States, while full-owners are farming fewer acres. This shift in ownership is a potential cause for concern because some previous research indicated that tenant and part-owner farmers were less likely to adopt conservation practices than farmers who owned the land they farmed. If that trend persists, ownership changes would signal a national drop in conservation adoption. Here we examine this issue using a survey of agricultural operators in the Clear Creek watershed in Iowa, a state with intensive agricultural production. We compare adoption of conservation practices, and preferences for conservation information sources and communication channels, between farmers who rent some portion of the land they farm (tenants and part-owners) and farmers who own all of the land they farm (full-owners). We find that renters are more likely to practice conservation tillage than full-owners, though they are less likely to rotate crops. In addition, renters report using federal government employees (specifically, Natural Resource Conservation Service and Farm Service Agency) as their primary sources of conservation information, while full-owners most frequently rely on neighbors, friends, and County Extension. These findings are significant for conservation policy because, unlike some past research, they indicate that renters are not resistant to all types of conservation practices, echoing recent studies finding an increase in conservation adoption among non-full-owners. Our results emphasize the importance of government conservation communication and can inform outreach efforts by helping tailor effective, targeted conservation strategies for owners and renters.

Linearization of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.

2009-01-01

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

E = Mc(super 2) for the Chemist: When is Mass Conserved?

ERIC Educational Resources Information Center

Treptow. Richard S.

2005-01-01

An equation derived by Albert Einstein in 1905 that expresses a relationship between mass and energy, formulated as E = mc(super 2) is discussed with reference to the extent mass is conserved. This query can be used to challenge students and develop their language and critical thinking skills.

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.

Documentation of the Fourth Order Band Model

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.; Hoitsma, D.

1979-01-01

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

Titration Calculations with Computer Algebra Software

ERIC Educational Resources Information Center

Lachance, Russ; Biaglow, Andrew

2012-01-01

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

THOR: an open-source exo-GCM

NASA Astrophysics Data System (ADS)

Grosheintz, Luc; Mendonça, João; Käppeli, Roger; Lukas Grimm, Simon; Mishra, Siddhartha; Heng, Kevin

2015-12-01

In this talk, I will present THOR, the first fully conservative, GPU-accelerated exo-GCM (general circulation model) on a nearly uniform, global grid that treats shocks and is non-hydrostatic. THOR will be freely available to the community as a standard tool.Unlike most GCMs THOR solves the full, non-hydrostatic Euler equations instead of the primitive equations. The equations are solved on a global three-dimensional icosahedral grid by a second order Finite Volume Method (FVM). Icosahedral grids are nearly uniform refinements of an icosahedron. We've implemented three different versions of this grid. FVM conserves the prognostic variables (density, momentum and energy) exactly and doesn't require a diffusion term (artificial viscosity) in the Euler equations to stabilize our solver. Historically FVM was designed to treat discontinuities correctly. Hence it excels at resolving shocks, including those present in hot exoplanetary atmospheres.Atmospheres are generally in near hydrostatic equilibrium. We therefore implement a well-balancing technique recently developed at the ETH Zurich. This well-balancing ensures that our FVM maintains hydrostatic equilibrium to machine precision. Better yet, it is able to resolve pressure perturbations from this equilibrium as small as one part in 100'000. It is important to realize that these perturbations are significantly smaller than the truncation error of the same scheme without well-balancing. If during the course of the simulation (due to forcing) the atmosphere becomes non-hydrostatic, our solver continues to function correctly.THOR just passed an important mile stone. We've implemented the explicit part of the solver. The explicit solver is useful to study instabilities or local problems on relatively short time scales. I'll show some nice properties of the explicit THOR. An explicit solver is not appropriate for climate study because the time step is limited by the sound speed. Therefore, we are working on the first fully implicit GCM. By ESS3, I hope to present results for the advection equation.THOR is part of the Exoclimes Simulation Platform (ESP), a set of open-source community codes for simulating and understanding the atmospheres of exoplanets. The ESP also includes tools for radiative transfer and retrieval (HELIOS), an opacity calculator (HELIOS-K), and a chemical kinetics solver (VULCAN). We expect to publicly release an initial version of THOR in 2016 on www.exoclime.org.

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

NASA Technical Reports Server (NTRS)

Barth, Timothy; Charrier, Pierre; Mansour, Nagi N. (Technical Monitor)

2001-01-01

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

The method of space-time and conservation element and solution element: A new approach for solving the Navier-Stokes and Euler equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1995-01-01

A new numerical framework for solving conservation laws is being developed. This new framework differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to overcome several key limitations of the above traditional methods. A two-level scheme for solving the convection-diffusion equation is constructed and used to illuminate the major differences between the present method and those previously mentioned. This explicit scheme, referred to as the a-mu scheme, has two independent marching variables.

Lateral Load Capacity of Piles: A Comparative Study Between Indian Standards and Theoretical Approach

NASA Astrophysics Data System (ADS)

Jayasree, P. K.; Arun, K. V.; Oormila, R.; Sreelakshmi, H.

2018-05-01

As per Indian Standards, laterally loaded piles are usually analysed using the method adopted by IS 2911-2010 (Part 1/Section 2). But the practising engineers are of the opinion that the IS method is very conservative in design. This work aims at determining the extent to which the conventional IS design approach is conservative. This is done through a comparative study between IS approach and the theoretical model based on Vesic's equation. Bore log details for six different bridges were collected from the Kerala Public Works Department. Cast in situ fixed head piles embedded in three soil conditions both end bearing as well as friction piles were considered and analyzed separately. Piles were also modelled in STAAD.Pro software based on IS approach and the results were validated using Matlock and Reese (In Proceedings of fifth international conference on soil mechanics and foundation engineering, 1961) equation. The results were presented as the percentage variation in values of bending moment and deflection obtained by different methods. The results obtained from the mathematical model based on Vesic's equation and that obtained as per the IS approach were compared and the IS method was found to be uneconomical and conservative.

A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

DOE PAGES

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...

2015-02-24

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less

Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows.

PubMed

Abel, I G; Plunk, G G; Wang, E; Barnes, M; Cowley, S C; Dorland, W; Schekochihin, A A

2013-11-01

This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ε = ρi/α of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad-Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the 'high-flow' gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.

Energy and maximum norm estimates for nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Olsson, Pelle; Oliger, Joseph

1994-01-01

We have devised a technique that makes it possible to obtain energy estimates for initial-boundary value problems for nonlinear conservation laws. The two major tools to achieve the energy estimates are a certain splitting of the flux vector derivative f(u)(sub x), and a structural hypothesis, referred to as a cone condition, on the flux vector f(u). These hypotheses are fulfilled for many equations that occur in practice, such as the Euler equations of gas dynamics. It should be noted that the energy estimates are obtained without any assumptions on the gradient of the solution u. The results extend to weak solutions that are obtained as point wise limits of vanishing viscosity solutions. As a byproduct we obtain explicit expressions for the entropy function and the entropy flux of symmetrizable systems of conservation laws. Under certain circumstances the proposed technique can be applied repeatedly so as to yield estimates in the maximum norm.

Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity

NASA Astrophysics Data System (ADS)

Thiele, Uwe; Archer, Andrew J.; Robbins, Mark J.; Gomez, Hector; Knobloch, Edgar

2013-04-01

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature versus mean order parameter plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The results are related to the phenomenon of slanted snaking but take the form of standard homoclinic snaking when the mean order parameter is plotted as a function of the chemical potential, and are expected to carry over to related models with a conserved order parameter.

Control volume based hydrocephalus research; analysis of human data

NASA Astrophysics Data System (ADS)

Cohen, Benjamin; Wei, Timothy; Voorhees, Abram; Madsen, Joseph; Anor, Tomer

2010-11-01

Hydrocephalus is a neuropathophysiological disorder primarily diagnosed by increased cerebrospinal fluid volume and pressure within the brain. To date, utilization of clinical measurements have been limited to understanding of the relative amplitude and timing of flow, volume and pressure waveforms; qualitative approaches without a clear framework for meaningful quantitative comparison. Pressure volume models and electric circuit analogs enforce volume conservation principles in terms of pressure. Control volume analysis, through the integral mass and momentum conservation equations, ensures that pressure and volume are accounted for using first principles fluid physics. This approach is able to directly incorporate the diverse measurements obtained by clinicians into a simple, direct and robust mechanics based framework. Clinical data obtained for analysis are discussed along with data processing techniques used to extract terms in the conservation equation. Control volume analysis provides a non-invasive, physics-based approach to extracting pressure information from magnetic resonance velocity data that cannot be measured directly by pressure instrumentation.

Three-pattern decomposition of global atmospheric circulation: part II—dynamical equations of horizontal, meridional and zonal circulations

NASA Astrophysics Data System (ADS)

Hu, Shujuan; Cheng, Jianbo; Xu, Ming; Chou, Jifan

2018-04-01

The three-pattern decomposition of global atmospheric circulation (TPDGAC) partitions three-dimensional (3D) atmospheric circulation into horizontal, meridional and zonal components to study the 3D structures of global atmospheric circulation. This paper incorporates the three-pattern decomposition model (TPDM) into primitive equations of atmospheric dynamics and establishes a new set of dynamical equations of the horizontal, meridional and zonal circulations in which the operator properties are studied and energy conservation laws are preserved, as in the primitive equations. The physical significance of the newly established equations is demonstrated. Our findings reveal that the new equations are essentially the 3D vorticity equations of atmosphere and that the time evolution rules of the horizontal, meridional and zonal circulations can be described from the perspective of 3D vorticity evolution. The new set of dynamical equations includes decomposed expressions that can be used to explore the source terms of large-scale atmospheric circulation variations. A simplified model is presented to demonstrate the potential applications of the new equations for studying the dynamics of the Rossby, Hadley and Walker circulations. The model shows that the horizontal air temperature anomaly gradient (ATAG) induces changes in meridional and zonal circulations and promotes the baroclinic evolution of the horizontal circulation. The simplified model also indicates that the absolute vorticity of the horizontal circulation is not conserved, and its changes can be described by changes in the vertical vorticities of the meridional and zonal circulations. Moreover, the thermodynamic equation shows that the induced meridional and zonal circulations and advection transport by the horizontal circulation in turn cause a redistribution of the air temperature. The simplified model reveals the fundamental rules between the evolution of the air temperature and the horizontal, meridional and zonal components of global atmospheric circulation.

Conservative 3 + 1 general relativistic variable Eddington tensor radiation transport equations

DOE PAGES

Cardall, Christian Y.; Endeve, Eirik; Mezzacappa, Anthony

2013-05-07

We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These equations are intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are the lab frame coordinate basis spacetime position coordinates and the particle energy measured in the comoving frame. With an eye towards astrophysical applications—such as core-collapse supernovae and compact object mergers—in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles aremore » neutrinos, we pay special attention to the consistency of four-momentum and lepton number exchange between neutrinos and the fluid, showing the term-by-term cancellations that must occur for this consistency to be achieved.« less

Modulational instability: Conservation laws and bright soliton solution of ion-acoustic waves in electron-positron-ion-dust plasmas

NASA Astrophysics Data System (ADS)

EL-Kalaawy, O. H.

2018-02-01

We consider the nonlinear propagation of non-planar (cylindrical and spherical) ion-acoustic (IA) envelope solitary waves in an unmagnetized plasma consisting of electron-positron-ion-dust plasma with two-electron temperature distributions in the context of the non-extensive statistics. The basic set of fluid equations is reduced to the modified nonlinear Schrödinger (MNLS) equation in cylindrical and spherical geometry by using the reductive perturbation method (RPM). It is found that the nature of the modulational instabilities would be significantly modified due to the effects of the non-extensive and other plasma parameters as well as cylindrical and spherical geometry. Conservation laws of the MNLS equation are obtained by Lie symmetry and multiplier method. A new exact solution (envelope bright soliton) is obtained by the extended homogeneous balance method. Finally, we study the results of this article.

A spectral mimetic least-squares method

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

Bochev, Pavel; Gerritsma, Marc

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

A spectral mimetic least-squares method

DOE PAGES

Bochev, Pavel; Gerritsma, Marc

2014-09-01

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

Lax pair, conservation laws and solitons for a (2 + 1)-dimensional fourth-order nonlinear Schrödinger equation governing an α-helical protein

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong

2015-11-01

Energy transfer through a (2+1)-dimensional α-helical protein can be described by a (2+1)-dimensional fourth-order nonlinear Schrödinger equation. For such an equation, a Lax pair and the infinitely-many conservation laws are derived. Using an auxiliary function and a bilinear formulation, we get the one-, two-, three- and N-soliton solutions via the Hirota method. The soliton velocity is linearly related to the lattice parameter γ, while the soliton' direction and amplitude do not depend on γ. Interactions between the two solitons are elastic, while those among the three solitons are pairwise elastic. Oblique, head-on and overtaking interactions between the two solitons are displayed. Oblique interaction among the three solitons and interactions among the two parallel solitons and a single one are presented as well.

Pinching solutions of slender cylindrical jets

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.; Orellana, Oscar

1993-01-01

Simplified equations for slender jets are derived for a circular jet of one fluid flowing into an ambient second fluid, the flow being confined in a circular tank. Inviscid flows are studied which include both surface tension effects and Kelvin-Helmholtz instability. For slender jets a coupled nonlinear system of equations is found for the jet shape and the axial velocity jump across it. The equations can break down after a finite time and similarity solutions are constructed, and studied analytically and numerically. The break-ups found pertain to the jet pinching after a finite time, without violation of the slender jet ansatz. The system is conservative and admissible singular solutions are those which conserve the total energy, mass, and momentum. Such solutions are constructed analytically and numerically, and in the case of vortex sheets with no surface tension certain solutions are given in closed form.

A Runge-Kutta discontinuous finite element method for high speed flows

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. T.

1991-01-01

A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.

Quantitative Compactness Estimates for Hamilton-Jacobi Equations

NASA Astrophysics Data System (ADS)

Ancona, Fabio; Cannarsa, Piermarco; Nguyen, Khai T.

2016-02-01

We study quantitative compactness estimates in {W^{1,1}_{loc}} for the map {S_t}, {t > 0} that is associated with the given initial data {u_0in Lip (R^N)} for the corresponding solution {S_t u_0} of a Hamilton-Jacobi equation u_t+Hbig(nabla_{x} ubig)=0, qquad t≥ 0,quad xinR^N, with a uniformly convex Hamiltonian {H=H(p)}. We provide upper and lower estimates of order {1/\\varepsilon^N} on the Kolmogorov {\\varepsilon}-entropy in {W^{1,1}} of the image through the map S t of sets of bounded, compactly supported initial data. Estimates of this type are inspired by a question posed by Lax (Course on Hyperbolic Systems of Conservation Laws. XXVII Scuola Estiva di Fisica Matematica, Ravello, 2002) within the context of conservation laws, and could provide a measure of the order of "resolution" of a numerical method implemented for this equation.

Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes

NASA Astrophysics Data System (ADS)

Chertock, Alina; Cui, Shumo; Kurganov, Alexander; Özcan, Şeyma Nur; Tadmor, Eitan

2018-04-01

We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples.

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.

Electromagnetic energy momentum in dispersive media

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

Philbin, T. G.

2011-01-15

The standard derivations of electromagnetic energy and momentum in media take Maxwell's equations as the starting point. It is well known that for dispersive media this approach does not directly yield exact expressions for the energy and momentum densities. Although Maxwell's equations fully describe electromagnetic fields, the general approach to conserved quantities in field theory is not based on the field equations, but rather on the action. Here an action principle for macroscopic electromagnetism in dispersive, lossless media is used to derive the exact conserved energy-momentum tensor. The time-averaged energy density reduces to Brillouin's simple formula when the fields aremore » monochromatic. The time-averaged momentum density for monochromatic fields corresponds to the familiar Minkowski expression DxB, but for general fields in dispersive media the momentum density does not have the Minkowski value. The results are unaffected by the debate over momentum balance in light-matter interactions.« less

Measuring the equations of state in a relaxed magnetohydrodynamic plasma.

PubMed

Kaur, M; Barbano, L J; Suen-Lewis, E M; Shrock, J E; Light, A D; Brown, M R; Schaffner, D A

2018-01-01

We report measurements of the equations of state of a fully relaxed magnetohydrodynamic (MHD) laboratory plasma. Parcels of magnetized plasma, called Taylor states, are formed in a coaxial magnetized plasma gun, and are allowed to relax and drift into a closed flux conserving volume. Density, ion temperature, and magnetic field are measured as a function of time as the Taylor states compress and heat. The theoretically predicted MHD and double adiabatic equations of state are compared to experimental measurements. We find that the MHD equation of state is inconsistent with our data.

On the various forms of the energy equation for a dilute, monatomic mixture of nonreacting gases

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.

1994-01-01

In the case of gas mixtures, the governing equations become rather formidable and a complete listing of the equations in their various forms and methods to evaluate the transport coefficients is difficult to find. This paper seeks to compile common, as well as less well known, results in a single document. Various relationships between equations describing conservation of energy for a dilute, monatomic, nonreacting gas in local equilibrium are provided. The gas is treated as nonrelativistic, not subject to magnetic or electric fields, or radiative effects.

Measuring the equations of state in a relaxed magnetohydrodynamic plasma

NASA Astrophysics Data System (ADS)

Kaur, M.; Barbano, L. J.; Suen-Lewis, E. M.; Shrock, J. E.; Light, A. D.; Brown, M. R.; Schaffner, D. A.

2018-01-01

We report measurements of the equations of state of a fully relaxed magnetohydrodynamic (MHD) laboratory plasma. Parcels of magnetized plasma, called Taylor states, are formed in a coaxial magnetized plasma gun, and are allowed to relax and drift into a closed flux conserving volume. Density, ion temperature, and magnetic field are measured as a function of time as the Taylor states compress and heat. The theoretically predicted MHD and double adiabatic equations of state are compared to experimental measurements. We find that the MHD equation of state is inconsistent with our data.

Spatial evolution of quantum mechanical states

NASA Astrophysics Data System (ADS)

Christensen, N. D.; Unger, J. E.; Pinto, S.; Su, Q.; Grobe, R.

2018-02-01

The time-dependent Schrödinger equation is solved traditionally as an initial-time value problem, where its solution is obtained by the action of the unitary time-evolution propagator on the quantum state that is known at all spatial locations but only at t = 0. We generalize this approach by examining the spatial evolution from a state that is, by contrast, known at all times t, but only at one specific location. The corresponding spatial-evolution propagator turns out to be pseudo-unitary. In contrast to the real energies that govern the usual (unitary) time evolution, the spatial evolution can therefore require complex phases associated with dynamically relevant solutions that grow exponentially. By introducing a generalized scalar product, for which the spatial generator is Hermitian, one can show that the temporal integral over the probability current density is spatially conserved, in full analogy to the usual norm of the state, which is temporally conserved. As an application of the spatial propagation formalism, we introduce a spatial backtracking technique that permits us to reconstruct any quantum information about an atom from the ionization data measured at a detector outside the interaction region.

76 FR 20089 - Energy Conservation Program: Energy Conservation Standards for Fluorescent Lamp Ballasts

Federal Register 2010, 2011, 2012, 2013, 2014

2011-04-11

... = high output. ** The proposed standards are based on an equation that is a function of the natural... High estimate Discount rate (emerging (existing Primary estimate technologies, roll- technologies, up...$) is the average of the low and high values used in DOE's analysis. [dagger] Total Benefits for both...

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

Eldred, Christopher; Randall, David

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restrictedmore » to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Lastly, detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.« less

An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes

DOE PAGES

Taitano, William; Chacon, Luis; Simakov, Andrei Nikolaevich

2016-04-25

In this paper, we propose an adaptive velocity-space discretization scheme for the multi-species, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass-, momentum-, and energy-conserving. Unlike most earlier studies, our approach normalizes the velocity-space coordinate to the temporally varying individual plasma species' local thermal velocity, v th (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic v th -ratio-based expansion ofmore » the Rosenbluth potentials that only requires the computation of several velocity-space integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocity-grid adaptivity and asymptotic expansions delivers many orders-of-magnitude savings in mesh resolution requirements compared to a single, static uniform mesh.« less

Numerical and experimental investigation of the 3D free surface flow in a model Pelton turbine

NASA Astrophysics Data System (ADS)

Fiereder, R.; Riemann, S.; Schilling, R.

2010-08-01

This investigation focuses on the numerical and experimental analysis of the 3D free surface flow in a Pelton turbine. In particular, two typical flow conditions occurring in a full scale Pelton turbine - a configuration with a straight inlet as well as a configuration with a 90 degree elbow upstream of the nozzle - are considered. Thereby, the effect of secondary flow due to the 90 degree bending of the upstream pipe on the characteristics of the jet is explored. The hybrid flow field consists of pure liquid flow within the conduit and free surface two component flow of the liquid jet emerging out of the nozzle into air. The numerical results are validated against experimental investigations performed in the laboratory of the Institute of Fluid Mechanics (FLM). For the numerical simulation of the flow the in-house unstructured fully parallelized finite volume solver solver3D is utilized. An advanced interface capturing model based on the classic Volume of Fluid method is applied. In order to ensure sharp interface resolution an additional convection term is added to the transport equation of the volume fraction. A collocated variable arrangement is used and the set of non-linear equations, containing fluid conservation equations and model equations for turbulence and volume fraction, are solved in a segregated manner. For pressure-velocity coupling the SIMPLE and PISO algorithms are implemented. Detailed analysis of the observed flow patterns in the jet and of the jet geometry are presented.

Evaluation of friction heating in cavitating high pressure Diesel injector nozzles

NASA Astrophysics Data System (ADS)

Salemi, R.; Koukouvinis, P.; Strotos, G.; McDavid, R.; Wang, Lifeng; Li, Jason; Marengo, M.; Gavaises, M.

2015-12-01

Variation of fuel properties occurring during extreme fuel pressurisation in Diesel fuel injectors relative to those under atmospheric pressure and room temperature conditions may affect significantly fuel delivery, fuel injection temperature, injector durability and thus engine performance. Indicative results of flow simulations during the full injection event of a Diesel injector are presented. In addition to the Navier-Stokes equations, the enthalpy conservation equation is considered for predicting the fuel temperature. Cavitation is simulated using an Eulerian-Lagrangian cavitation model fully coupled with the flow equations. Compressible bubble dynamics based on the R-P equation also consider thermal effects. Variable fuel properties function of the local pressure and temperature are taken from literature and correspond to a reference so-called summer Diesel fuel. Fuel pressurisation up to 3000bar pressure is considered while various wall temperature boundary conditions are tested in order to compare their effect relative to those of the fuel heating caused during the depressurisation of the fuel as it passes through the injection orifices. The results indicate formation of strong temperature gradients inside the fuel injector while heating resulting from the extreme friction may result to local temperatures above the fuel's boiling point. Predictions indicate bulk fuel temperature increase of more than 100°C during the opening phase of the needle valve. Overall, it is concluded that such effects are significant for the injector performance and should be considered in relevant simulation tools.

Molecular Dynamic Simulation of Water Vapor and Determination of Diffusion Characteristics in the Pore

NASA Astrophysics Data System (ADS)

Nikonov, Eduard G.; Pavluš, Miron; Popovičová, Mária

2018-02-01

One of the varieties of pores, often found in natural or artificial building materials, are the so-called blind pores of dead-end or saccate type. Three-dimensional model of such kind of pore has been developed in this work. This model has been used for simulation of water vapor interaction with individual pore by molecular dynamics in combination with the diffusion equation method. Special investigations have been done to find dependencies between thermostats implementations and conservation of thermodynamic and statistical values of water vapor - pore system. The two types of evolution of water - pore system have been investigated: drying and wetting of the pore. Full research of diffusion coefficient, diffusion velocity and other diffusion parameters has been made.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Kinetic description of ionospheric dynamics in the three-fluid approximation

NASA Technical Reports Server (NTRS)

Comfort, R. H.

1975-01-01

Conservation equations are developed in the three-fluid approximation for general application problems of ionospheric dynamics in the altitude region 90 km to 800 km for all geographic locations. These equations are applied to a detailed study of auroral E region neutral winds and their relationship to ionospheric plasma motions.

Program For Finite-Element Analyses Of Phase-Change Fluids

NASA Technical Reports Server (NTRS)

Viterna, L. A.

1995-01-01

PHASTRAN analyzes heat-transfer and flow behaviors of materials undergoing phase changes. Many phase changes operate over range of accelerations or effective gravitational fields. To analyze such thermal systems, it is necessary to obtain simultaneous solutions for equations of conservation of energy, momentum, and mass, and for equation of state. Written in APL2.

Steady-state heat conduction in quiescent fluids: Incompleteness of the Navier-Stokes-Fourier equations

NASA Astrophysics Data System (ADS)

Brenner, Howard

2011-10-01

Linear irreversible thermodynamic principles are used to demonstrate, by counterexample, the existence of a fundamental incompleteness in the basic pre-constitutive mass, momentum, and energy equations governing fluid mechanics and transport phenomena in continua. The demonstration is effected by addressing the elementary case of steady-state heat conduction (and transport processes in general) occurring in quiescent fluids. The counterexample questions the universal assumption of equality of the four physically different velocities entering into the basic pre-constitutive mass, momentum, and energy conservation equations. Explicitly, it is argued that such equality is an implicit constitutive assumption rather than an established empirical fact of unquestioned authority. Such equality, if indeed true, would require formal proof of its validity, currently absent from the literature. In fact, our counterexample shows the assumption of equality to be false. As the current set of pre-constitutive conservation equations appearing in textbooks are regarded as applicable both to continua and noncontinua (e.g., rarefied gases), our elementary counterexample negating belief in the equality of all four velocities impacts on all aspects of fluid mechanics and transport processes, continua and noncontinua alike.

Variational formulation for dissipative continua and an incremental J-integral

NASA Astrophysics Data System (ADS)

Rahaman, Md. Masiur; Dhas, Bensingh; Roy, D.; Reddy, J. N.

2018-01-01

Our aim is to rationally formulate a proper variational principle for dissipative (viscoplastic) solids in the presence of inertia forces. As a first step, a consistent linearization of the governing nonlinear partial differential equations (PDEs) is carried out. An additional set of complementary (adjoint) equations is then formed to recover an underlying variational structure for the augmented system of linearized balance laws. This makes it possible to introduce an incremental Lagrangian such that the linearized PDEs, including the complementary equations, become the Euler-Lagrange equations. Continuous groups of symmetries of the linearized PDEs are computed and an analysis is undertaken to identify the variational groups of symmetries of the linearized dissipative system. Application of Noether's theorem leads to the conservation laws (conserved currents) of motion corresponding to the variational symmetries. As a specific outcome, we exploit translational symmetries of the functional in the material space and recover, via Noether's theorem, an incremental J-integral for viscoplastic solids in the presence of inertia forces. Numerical demonstrations are provided through a two-dimensional plane strain numerical simulation of a compact tension specimen of annealed mild steel under dynamic loading.

Involution and Difference Schemes for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.

In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

Numerical Examination of Flux Correction for Solving the Navier-Stokes Equations on Unstructured Meshes

DTIC Science & Technology

2014-08-29

lends itself to parallelization due to it’s discontinuous nature [27]. It has well-established stability properties and is actively being researched...from considering Conservation of Mass , Conservation of Momentum, and Conservation of Energy. This well-known result, known as the Navier-Stokes...internal plus kinetic) per unit mass and h = e+ Pρ as the enthalpy. qj is the jth component of the heat flux vector. This can be related to temperature

Reduced Basis and Stochastic Modeling of Liquid Propellant Rocket Engine as a Complex System

DTIC Science & Technology

2015-07-02

additions, the approach will be extended to a real- gas system so that it can be used to investigate model multi-element liquid rocket combustors in a...Sirignano (2010). In the following discussion, we examine the various conservation principles for the gas and liquid phases. The hyperbolic nature of the...conservation equations for the gas and liquid phases. Mass conservation of individual chemical species or of individual classes of liquid droplets will

HYDRA-II: A hydrothermal analysis computer code: Volume 3, Verification/validation assessments

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

McCann, R.A.; Lowery, P.S.

1987-10-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equationsmore » for conservation of momentum are enhanced by the incorporation of directional porosities and permeabilities that aid in modeling solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated procedures are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume I - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. Volume II - User's Manual contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a model problem. This volume, Volume III - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. This volume also documents comparisons between the results of simulations of single- and multiassembly storage systems and actual experimental data. 11 refs., 55 figs., 13 tabs.« less

High-Resolution Genuinely Multidimensional Solution of Conservation Laws by the Space-Time Conservation Element and Solution Element Method

NASA Technical Reports Server (NTRS)

Himansu, Ananda; Chang, Sin-Chung; Yu, Sheng-Tao; Wang, Xiao-Yen; Loh, Ching-Yuen; Jorgenson, Philip C. E.

1999-01-01

In this overview paper, we review the basic principles of the method of space-time conservation element and solution element for solving the conservation laws in one and two spatial dimensions. The present method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. In contrast to the modern upwind schemes, the approach here does not use the Riemann solver and the reconstruction procedure as the building blocks. The drawbacks of the upwind approach, such as the difficulty of rationally extending the 1D scalar approach to systems of equations and particularly to multiple dimensions is here contrasted with the uniformity and ease of generalization of the Conservation Element and Solution Element (CE/SE) 1D scalar schemes to systems of equations and to multiple spatial dimensions. The assured compatibility with the simplest type of unstructured meshes, and the uniquely simple nonreflecting boundary conditions of the present method are also discussed. The present approach has yielded high-resolution shocks, rarefaction waves, acoustic waves, vortices, ZND detonation waves, and shock/acoustic waves/vortices interactions. Moreover, since no directional splitting is employed, numerical resolution of two-dimensional calculations is comparable to that of the one-dimensional calculations. Some sample applications displaying the strengths and broad applicability of the CE/SE method are reviewed.

Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

NASA Astrophysics Data System (ADS)

Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.

2018-01-01

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

DOE PAGES

Su, Hongling; Li, Shengtai

2016-02-03

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

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

Su, Hongling; Li, Shengtai

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

An approximation of herd effect due to vaccinating children against seasonal influenza – a potential solution to the incorporation of indirect effects into static models

PubMed Central

2013-01-01

Background Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination. Methods Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals. Results The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation. Conclusions This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses. PMID:23339290

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations.

PubMed

Schüler, D; Alonso, S; Torcini, A; Bär, M

2014-12-01

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.

A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

NASA Astrophysics Data System (ADS)

Joshi, Vaibhav; Jaiman, Rajeev K.

2018-05-01

We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase-field solver for a practical offshore engineering application of wave-structure interaction.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

Real-Gas Effects on Binary Mixing Layers

NASA Technical Reports Server (NTRS)

Okong'o, Nora; Bellan, Josette

2003-01-01

This paper presents a computational study of real-gas effects on the mean flow and temporal stability of heptane/nitrogen and oxygen/hydrogen mixing layers at supercritical pressures. These layers consist of two counterflowing free streams of different composition, temperature, and density. As in related prior studies reported in NASA Tech Briefs, the governing conservation equations were the Navier-Stokes equations of compressible flow plus equations for the conservation of total energy and of chemical- species masses. In these equations, the expressions for heat fluxes and chemical-species mass fluxes were derived from fluctuation-dissipation theory and incorporate Soret and Dufour effects. Similarity equations for the streamwise velocity, temperature, and mass fractions were derived as approximations to the governing equations. Similarity profiles showed important real-gas, non-ideal-mixture effects, particularly for temperature, in departing from the error-function profile, which is the similarity solution for incompressible flow. The temperature behavior was attributed to real-gas thermodynamics and variations in Schmidt and Prandtl numbers. Temporal linear inviscid stability analyses were performed using the similarity and error-function profiles as the mean flow. For the similarity profiles, the growth rates were found to be larger and the wavelengths of highest instability shorter, relative to those of the errorfunction profiles and to those obtained from incompressible-flow stability analysis. The range of unstable wavelengths was found to be larger for the similarity profiles than for the error-function profiles

Thermobaricity, cabbeling, and water-mass conversion

NASA Astrophysics Data System (ADS)

McDougall, Trevor J.

1987-05-01

The efficient mixing of heat and salt along neutral surfaces (by mesoscale eddies) is shown to lead to vertical advection through these neutral surfaces. This is due to the nonlinearities of the equation of state of seawater through terms like ∂2ρ/∂θ∂p (thermobaric effect) and ∂2ρ/∂ θ2 (cabbeling). Cabbeling always causes a sinking or downwelling of fluid through neutral surfaces, whereas thermobaricity can lead to a vertical velocity (relative to neutral surfaces) of either sign. In this paper it is shown that for reasonable values of the lateral scalar diffusivity (especially below a depth of 1000 m), these two processes cause vertical velocities of the order of 10-7 m s-1 through neutral surfaces (usually downward!) and cause water-mass conversion of a magnitude equal to that caused by a vertical diffusivity of 10-4 m2 s-1 (often equivalent to a negative diffusivity). Both thermobaricity and cabbeling can occur in the presence of any nonzero amount of small-scale turbulence and so will not be detected by microstructure measurements. The conservation equations for tracers are considered in a nonorthogonal coordinate frame that moves with neutral surfaces in the ocean. Since only mixing processes cause advection across neutral surfaces, it is useful to regard this vertical advection as a symptom of various mixing processes rather than as a separate physical process. It is possible to derive conservative equations for scalars that do not contain the vertical advective term explicity. In these conservation equations, the terms that represent mixing processes are substantially altered. It is argued that this form of the conservation equations is the most appropriate when considering water-mass transformation, and some examples are given of its application in the North Atlantic. It is shown that the variation of the vertical diffusivity with height does not cause water-mass transformation. Also, salt fingering is often 3-4 times more effective at changing the potential temperature of a water mass than would be implied by simply calculating the vertical derivative of the fingering heat flux.

Entropy Splitting and Numerical Dissipation

NASA Technical Reports Server (NTRS)

Yee, H. C.; Vinokur, M.; Djomehri, M. J.

1999-01-01

A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock-turbulence interactions. The fourth is to determine if this method can be extended to other physical equations of state and other evolutionary equation sets. If numerical dissipation is needed, the Yee, Sandham, and Djomehri (1999) numerical dissipation is employed. The Yee et al. schemes fit in the Olsson and Oliger framework.

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

Conservation of wave action. [in discrete oscillating system

NASA Technical Reports Server (NTRS)

Hayes, W. D.

1974-01-01

It is pointed out that two basic principles appear in the theory of wave propagation, including the existence of a phase variable and a law governing the intensity, in terms of a conservation law. The concepts underlying such a conservation law are explored. The waves treated are conservative in the sense that they obey equations derivable from a variational principle applied to a Lagrangian functional. A discrete oscillating system is considered. The approach employed also permits in a natural way the definition of a local action density and flux in problems in which the waves are modal or general.

Part 1 of a Computational Study of a Drop-Laden Mixing Layer

NASA Technical Reports Server (NTRS)

Okong'o, Nora A.; Bellan, Josette

2004-01-01

This first of three reports on a computational study of a drop-laden temporal mixing layer presents the results of direct numerical simulations (DNS) of well-resolved flow fields and the derivation of the large-eddy simulation (LES) equations that would govern the larger scales of a turbulent flow field. The mixing layer consisted of two counterflowing gas streams, one of which was initially laden with evaporating liquid drops. The gas phase was composed of two perfect gas species, the carrier gas and the vapor emanating from the drops, and was computed in an Eulerian reference frame, whereas each drop was tracked individually in a Lagrangian manner. The flow perturbations that were initially imposed on the layer caused mixing and eventual transition to turbulence. The DNS database obtained included transitional states for layers with various liquid mass loadings. For the DNS, the gas-phase equations were the compressible Navier-Stokes equations for conservation of momentum and additional conservation equations for total energy and species mass. These equations included source terms representing the effect of the drops on the mass, momentum, and energy of the gas phase. From the DNS equations, the expression for the irreversible entropy production (dissipation) was derived and used to determine the dissipation due to the source terms. The LES equations were derived by spatially filtering the DNS set and the magnitudes of the terms were computed at transitional states, leading to a hierarchy of terms to guide simplification of the LES equations. It was concluded that effort should be devoted to the accurate modeling of both the subgridscale fluxes and the filtered source terms, which were the dominant unclosed terms appearing in the LES equations.

A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows

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

Owkes, Mark, E-mail: mfc86@cornell.edu; Desjardins, Olivier

2013-09-15

The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395–8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smallest possible computational stencil resulting in an accurate method with good parallel scaling. This work includes a DG implementation of the level set transport equation, which moves the level set with the flow field velocity, and a DG implementation of themore » reinitialization equation, which is used to maintain the shape of the level set profile to promote good mass conservation. A near second order converging interface curvature is obtained by following a height function methodology (common amongst volume of fluid schemes) in the context of the conservative level set. Various numerical experiments are conducted to test the properties of the method and show excellent results, even on coarse meshes. The tests include Zalesak’s disk, two-dimensional deformation of a circle, time evolution of a standing wave, and a study of the Kelvin–Helmholtz instability. Finally, this novel methodology is employed to simulate the break-up of a turbulent liquid jet.« less

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

A gravitational energy–momentum and the thermodynamic description of gravity

NASA Astrophysics Data System (ADS)

Acquaviva, G.; Kofroň, D.; Scholtz, M.

2018-05-01

A proposal for the gravitational energy–momentum tensor, known in the literature as the square root of Bel–Robinson tensor (SQBR), is analyzed in detail. Being constructed exclusively from the Weyl part of the Riemann tensor, such tensor encapsulates the geometric properties of free gravitational fields in terms of optical scalars of null congruences: making use of the general decomposition of any energy–momentum tensor, we explore the thermodynamic interpretation of such geometric quantities. While the matter energy–momentum is identically conserved due to Einstein’s field equations, the SQBR is not necessarily conserved and dissipative terms could arise in its vacuum continuity equation. We discuss the possible physical interpretations of such mathematical properties.

Conservative properties of finite difference schemes for incompressible flow

NASA Technical Reports Server (NTRS)

Morinishi, Youhei

1995-01-01

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

Conservative multizonal interface algorithm for the 3-D Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Molvik, G. A.

1991-01-01

A conservative zonal interface algorithm using features of both structured and unstructured mesh CFD technology is presented. The flow solver within each of the zones is based on structured mesh CFD technology. The interface algorithm was implemented into two three-dimensional Navier-Stokes finite volume codes and was found to yield good results.

Isogeometric Divergence-conforming B-splines for the Steady Navier-Stokes Equations

DTIC Science & Technology

2012-04-01

discretizations produce pointwise divergence-free velocity elds and hence exactly satisfy mass conservation. Consequently, discrete variational formulations...cretizations produce pointwise divergence-free velocity fields and hence exactly satisfy mass conservation. Consequently, discrete variational ... variational formulation. Using a combination of an advective for- mulation, SUPG, PSPG, and grad-div stabilization, provably convergent numerical methods

A fast, time-accurate unsteady full potential scheme

NASA Technical Reports Server (NTRS)

Shankar, V.; Ide, H.; Gorski, J.; Osher, S.

1985-01-01

The unsteady form of the full potential equation is solved in conservation form by an implicit method based on approximate factorization. At each time level, internal Newton iterations are performed to achieve time accuracy and computational efficiency. A local time linearization procedure is introduced to provide a good initial guess for the Newton iteration. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi, obtained by imposing the density to be continuous across the wake. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. The resulting unsteady method performs well which, even at low reduced frequency levels of 0.1 or less, requires fewer than 100 time steps per cycle at transonic Mach numbers. The code is fully vectorized for the CRAY-XMP and the VPS-32 computers.

A Summary of the Space-Time Conservation Element and Solution Element (CESE) Method

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen J.

2015-01-01

The space-time Conservation Element and Solution Element (CESE) method for solving conservation laws is examined for its development motivation and design requirements. The characteristics of the resulting scheme are discussed. The discretization of the Euler equations is presented to show readers how to construct a scheme based on the CESE method. The differences and similarities between the CESE method and other traditional methods are discussed. The strengths and weaknesses of the method are also addressed.

Separation of acoustic waves in isentropic flow perturbations

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

Henke, Christian, E-mail: christian.henke@atlas-elektronik.com

2015-04-15

The present contribution investigates the mechanisms of sound generation and propagation in the case of highly-unsteady flows. Based on the linearisation of the isentropic Navier–Stokes equation around a new pathline-averaged base flow, it is demonstrated for the first time that flow perturbations of a non-uniform flow can be split into acoustic and vorticity modes, with the acoustic modes being independent of the vorticity modes. Therefore, we can propose this acoustic perturbation as a general definition of sound. As a consequence of the splitting result, we conclude that the present acoustic perturbation is propagated by the convective wave equation and fulfilsmore » Lighthill’s acoustic analogy. Moreover, we can define the deviations of the Navier–Stokes equation from the convective wave equation as “true” sound sources. In contrast to other authors, no assumptions on a slowly varying or irrotational flow are necessary. Using a symmetry argument for the conservation laws, an energy conservation result and a generalisation of the sound intensity are provided. - Highlights: • First splitting of non-uniform flows in acoustic and non-acoustic components. • These result leads to a generalisation of sound which is compatible with Lighthill’s acoustic analogy. • A closed equation for the generation and propagation of sound is given.« less

An improved numerical method for the kernel density functional estimation of disperse flow

NASA Astrophysics Data System (ADS)

Smith, Timothy; Ranjan, Reetesh; Pantano, Carlos

2014-11-01

We present an improved numerical method to solve the transport equation for the one-point particle density function (pdf), which can be used to model disperse flows. The transport equation, a hyperbolic partial differential equation (PDE) with a source term, is derived from the Lagrangian equations for a dilute particle system by treating position and velocity as state-space variables. The method approximates the pdf by a discrete mixture of kernel density functions (KDFs) with space and time varying parameters and performs a global Rayleigh-Ritz like least-square minimization on the state-space of velocity. Such an approximation leads to a hyperbolic system of PDEs for the KDF parameters that cannot be written completely in conservation form. This system is solved using a numerical method that is path-consistent, according to the theory of non-conservative hyperbolic equations. The resulting formulation is a Roe-like update that utilizes the local eigensystem information of the linearized system of PDEs. We will present the formulation of the base method, its higher-order extension and further regularization to demonstrate that the method can predict statistics of disperse flows in an accurate, consistent and efficient manner. This project was funded by NSF Project NSF-DMS 1318161.

Evaluation of abutment scour prediction equations with field data

USGS Publications Warehouse

Benedict, S.T.; Deshpande, N.; Aziz, N.M.

2007-01-01

The U.S. Geological Survey, in cooperation with FHWA, compared predicted abutment scour depths, computed with selected predictive equations, with field observations collected at 144 bridges in South Carolina and at eight bridges from the National Bridge Scour Database. Predictive equations published in the 4th edition of Evaluating Scour at Bridges (Hydraulic Engineering Circular 18) were used in this comparison, including the original Froehlich, the modified Froehlich, the Sturm, the Maryland, and the HIRE equations. The comparisons showed that most equations tended to provide conservative estimates of scour that at times were excessive (as large as 158 ft). Equations also produced underpredictions of scour, but with less frequency. Although the equations provide an important resource for evaluating abutment scour at bridges, the results of this investigation show the importance of using engineering judgment in conjunction with these equations.

Two dimensional numerical prediction of deflagration-to-detonation transition in porous energetic materials.

PubMed

Narin, B; Ozyörük, Y; Ulas, A

2014-05-30

This paper describes a two-dimensional code developed for analyzing two-phase deflagration-to-detonation transition (DDT) phenomenon in granular, energetic, solid, explosive ingredients. The two-dimensional model is constructed in full two-phase, and based on a highly coupled system of partial differential equations involving basic flow conservation equations and some constitutive relations borrowed from some one-dimensional studies that appeared in open literature. The whole system is solved using an optimized high-order accurate, explicit, central-difference scheme with selective-filtering/shock capturing (SF-SC) technique, to augment central-diffencing and prevent excessive dispersion. The sources of the equations describing particle-gas interactions in terms of momentum and energy transfers make the equation system quite stiff, and hence its explicit integration difficult. To ease the difficulties, a time-split approach is used allowing higher time steps. In the paper, the physical model for the sources of the equation system is given for a typical explosive, and several numerical calculations are carried out to assess the developed code. Microscale intergranular and/or intragranular effects including pore collapse, sublimation, pyrolysis, etc. are not taken into account for ignition and growth, and a basic temperature switch is applied in calculations to control ignition in the explosive domain. Results for one-dimensional DDT phenomenon are in good agreement with experimental and computational results available in literature. A typical shaped-charge wave-shaper case study is also performed to test the two-dimensional features of the code and it is observed that results are in good agreement with those of commercial software. Copyright © 2014 Elsevier B.V. All rights reserved.

Solution of the Wang Chang-Uhlenbeck equation for molecular hydrogen

NASA Astrophysics Data System (ADS)

Anikin, Yu. A.

2017-06-01

Molecular hydrogen is modeled by numerically solving the Wang Chang-Uhlenbeck equation. The differential scattering cross sections of molecules are calculated using the quantum mechanical scattering theory of rigid rotors. The collision integral is computed by applying a fully conservative projection method. Numerical results for relaxation, heat conduction, and a one-dimensional shock wave are presented.

First Principles Modeling of the Performance of a Hydrogen-Peroxide-Driven Chem-E-Car

ERIC Educational Resources Information Center

Farhadi, Maryam; Azadi, Pooya; Zarinpanjeh, Nima

2009-01-01

In this study, performance of a hydrogen-peroxide-driven car has been simulated using basic conservation laws and a few numbers of auxiliary equations. A numerical method was implemented to solve sets of highly non-linear ordinary differential equations. Transient pressure and the corresponding traveled distance for three different car weights are…

Developing above-ground woody biomass equations for open-grown, multiple-stemmed tree species: shelterbelt-grown Russian-olive

Treesearch

Xinhau Zhour; James R. Brandle; Michele M. Schoeneberger; Tala Awada

2007-01-01

Multiple-stemmed tree species are often used in agricultural settings, playing a significant role in natural resource conservation and carbon sequestration. Biomass estimation, whether for modeling growth under different climate scenarios, accounting for carbon sequestered, or inclusion in natural resource inventories, requires equations that can accurately describe...

A Note on ;New Hierarchies of Integrable Lattice Equations and Associated Properties: Darboux Transformation Conservation Laws and Integrable Coupling; [Rep. Math. Phys. 67 (2011), 259

NASA Astrophysics Data System (ADS)

Xu, Xi-Xiang

2016-12-01

We prove that two new hierarchies of integrable lattice equations in [Rep. Math. Phys.67 (2011), 259] can be respectively changed into the famous relativistic Toda lattice hierarchies in the polynomial and the rational forms by means of a simple transformation.

Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves

NASA Technical Reports Server (NTRS)

Webb, G. M.; Brio, M.; Zank, G. P.

1995-01-01

In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.

A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Patel, N.

1983-01-01

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Weak solutions of the three-dimensional vorticity equation with vortex singularities

NASA Technical Reports Server (NTRS)

Winckelmans, G.; Leonard, A.

1988-01-01

The extension of the concept of vortex singularities, developed by Saffman and Meiron (1986) for the case of two-dimensional point vortices in an incompressible vortical flow, to the three-dimensional case of vortex sticks (vortons) is investigated analytically. The derivation of the governing equations is explained, and it is demonstrated that the formulation obtained conserves total vorticity and is a weak solution of the vorticity equation, making it an appropriate means for representing three-dimensional vortical flows with limited numbers of vortex singularities.

Extended symmetry analysis of generalized Burgers equations

NASA Astrophysics Data System (ADS)

Pocheketa, Oleksandr A.; Popovych, Roman O.

2017-10-01

Using enhanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form ut + uux + f(t, x)uxx = 0. This enhances all the previous results on symmetries of these equations and includes the description of admissible transformations, Lie symmetries, Lie and nonclassical reductions, hidden symmetries, conservation laws, potential admissible transformations, and potential symmetries. The study is based on the fact that the class is normalized, and its equivalence group is finite-dimensional.

Numerical solution of a coupled pair of elliptic equations from solid state electronics

NASA Technical Reports Server (NTRS)

Phillips, T. N.

1983-01-01

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

Involving the Navier-Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method.

PubMed

Verschaeve, Joris C G

2011-06-13

By means of the continuity equation of the incompressible Navier-Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

INTERNATIONAL CONFERENCE ON SEMICONDUCTOR INJECTION LASERS SELCO-87: Pulsations of light emitted by laser diodes

NASA Astrophysics Data System (ADS)

Enders, P.

1988-11-01

A system of three simple rate equations, derived from equations describing the excess heating near the front face of a resonator, is used as a model of the appearance of spontaneous (self-sustained) pulsations of light emitted by injection lasers. The rate equations are considered as an almost conservative system and the limit cycle is calculated for the system. The good agreement with numerical results favors our approximation, compared with other approximate calculations.

Entropy jump across an inviscid shock wave

NASA Technical Reports Server (NTRS)

Salas, Manuel D.; Iollo, Angelo

1995-01-01

The shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure are shown to be the same, however density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy, propagation equation cannot be used as a conservation law.

Synthesis of Refractory Compounds with Gasless Combustion Reactions.

DTIC Science & Technology

1983-09-01

either Al or Mg as the reducing agent. With Al as the reductant, the stoichiometric equation is 2Mo03 + B203 + 6 Al 2MoB + 3 A120 3 Using the methods...r. rr. . . ;. ., .s . , . . o. . - •-~~- ~- . . . .4 calculated to be 267.3 kcal/mole. With Mg as the reductant, the stoichio- metric equation for the...reaction conditions also are assumed for each model. Conservation of energy and heat diffusion equations are applied to a characteristic control volume

Time domain convergence properties of Lyapunov stable penalty methods

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Sunkel, John

1991-01-01

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

Ex situ conservation of plant diversity in the world's botanic gardens.

PubMed

Mounce, Ross; Smith, Paul; Brockington, Samuel

2017-10-01

Botanic gardens conserve plant diversity ex situ and can prevent extinction through integrated conservation action. Here we quantify how that diversity is conserved in ex situ collections across the world's botanic gardens. We reveal that botanic gardens manage at least 105,634 species, equating to 30% of all plant species diversity, and conserve over 41% of known threatened species. However, we also reveal that botanic gardens are disproportionately temperate, with 93% of species held in the Northern Hemisphere. Consequently, an estimated 76% of species absent from living collections are tropical in origin. Furthermore, phylogenetic bias ensures that over 50% of vascular genera, but barely 5% of non-vascular genera, are conserved ex situ. While botanic gardens are discernibly responding to the threat of species extinction, just 10% of network capacity is devoted to threatened species. We conclude that botanic gardens play a fundamental role in plant conservation, but identify actions to enhance future conservation of biodiversity.

Pulsational mode fluctuations and their basic conservation laws

NASA Astrophysics Data System (ADS)

Borah, B.; Karmakar, P. K.

2015-01-01

We propose a theoretical hydrodynamic model for investigating the basic features of nonlinear pulsational mode stability in a partially charged dust molecular cloud within the framework of the Jeans homogenization assumption. The inhomogeneous cloud is modeled as a quasi-neutral multifluid consisting of the warm electrons, warm ions, and identical inertial cold dust grains with partial ionization in a neutral gaseous background. The grain-charge is assumed not to vary in the fluctuation evolution time scale. The active inertial roles of the thermal species are included. We apply a standard multiple scaling technique centered on the gravito-electrostatic equilibrium to understand the fluctuations on the astrophysical scales of space and time. This is found that electrostatic and self-gravitational eigenmodes co-exist as diverse solitary spectral patterns governed by a pair of Korteweg-de Vries (KdV) equations. In addition, all the relevant classical conserved quantities associated with the KdV system under translational invariance are methodologically derived and numerically analyzed. A full numerical shape-analysis of the fluctuations, scale lengths and perturbed densities with multi-parameter variation of judicious plasma conditions is carried out. A correlation of the perturbed densities and gravito-electrostatic spectral patterns is also graphically indicated. It is demonstrated that the solitary mass, momentum and energy densities also evolve like solitary spectral patterns which remain conserved throughout the spatiotemporal scales of the fluctuation dynamics. Astrophysical and space environments significant to our results are briefly highlighted.

Thermophysical Fluid Dynamics: the Key to the Structures of Fluid Objects

NASA Astrophysics Data System (ADS)

Houben, H.

2013-12-01

It has become customary to model the hydrodynamics of fluid planets like Jupiter and Saturn by spinning up general circulation models until they reach a statistical steady state. This approach is physically sound, based on the thermodynamic expectation that the system will eventually achieve a state of maximum entropy, but the models have not been specifically designed for this purpose. Over the course of long integrations, numerical artifacts can drive the system to a state that does not correspond to the physically realistic end state. A different formulation of the governing equations promises better results. The equations of motion are recast as scalar conservation laws in which the diabatic and irreversible terms (both entropy-changing) are clearly identified. The balance between these terms defines the steady state of the system analytically, without the need for any temporal integrations. The conservation of mass in this system is trivial. Conservation of angular momentum replaces the zonal momentum equation and determines the zonal wind from a balance between the tidal torque and frictional dissipation. The principle of wave-mean flow non-interaction is preserved. Bernoulli's Theorem replaces the energy equation. The potential temperature structure is determined by the balance between work done against friction and heat transfer by convection and radiation. An equation of state and the traditional momentum equations in the meridional plane are sufficient to complete the model. Based on the assumption that the final state vertical and meridional winds are small compared to the zonal wind (in any case they are impossible to predict ab initio as they are driven by wave flux convergences), these last equations determine the pressure and density (and hence gravity) fields of the basic state. The thermal wind relation (in its most general form with the axial derivative of the zonal wind balancing the baroclinicity) is preserved. The model is not hydrostatic (in the sense used in planetary modeling) and the zonal wind is not constant on cylinders. Rather, the zonal wind falls off more rapidly with depth --- at least as fast as r3. A similar reformulation of the equations of magnetohydrodynamics is possible. It is found that wave-mean flow non-interaction extends to Alfven waves. Bernoulli's Theorem is augmented by the Poynting Theorem. The components of the traditional dynamo equation can be written as conservation laws. Only a single element of the alpha tensor contributes to the generation of axisymmetric magnetic fields and the mean meridional circulation provides a significant feedback, quenching the omega effect and limiting the amplitudes of non-axisymmetric fields. Thus analytic models are available for all the state variables of Jupiter and Saturn. The unknown independent variables are terms in the equation of state, the eddy viscosity and heat transport coefficients, the magnetic resistivity, and the strength of the tidal torques (which are dependent on the vertical structure of the planet's troposphere). By making new measurements of the atmospheric structure and higher order gravitational moments of Jupiter, JUNO has the potential to constrain these unknowns and contribute greatly to our understanding of the interior of that planet.

On mass and momentum conservation in the variable-parameter Muskingum method

NASA Astrophysics Data System (ADS)

Reggiani, Paolo; Todini, Ezio; Meißner, Dennis

2016-12-01

In this paper we investigate mass and momentum conservation in one-dimensional routing models. To this end we formulate the conservation equations for a finite-dimensional reach and compute individual terms using three standard Saint-Venant (SV) solvers: SOBEK, HEC-RAS and MIKE11. We also employ two different variable-parameter Muskingum (VPM) formulations: the classical Muskingum-Cunge (MC) and the revised, mass-conservative Muskingum-Cunge-Todini (MCT) approach, whereby geometrical cross sections are treated analytically in both cases. We initially compare the three SV solvers for a straight mild-sloping prismatic channel with geometric cross sections and a synthetic hydrograph as boundary conditions against the analytical MC and MCT solutions. The comparison is substantiated by the fact that in this flow regime the conditions for the parabolic equation model solved by MC and MCT are met. Through this intercomparison we show that all approaches have comparable mass and momentum conservation properties, except the MC. Then we extend the MCT to use natural cross sections for a real irregular river channel forced by an observed triple-peak event and compare the results with SOBEK. The model intercomparison demonstrates that the VPM in the form of MCT can be a computationally efficient, fully mass and momentum conservative approach and therefore constitutes a valid alternative to Saint-Venant based flood wave routing for a wide variety of rivers and channels in the world when downstream boundary conditions or hydraulic structures are non-influential.

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

NASA Technical Reports Server (NTRS)

Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James

1992-01-01

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Background history and cosmic perturbations for a general system of self-conserved dynamical dark energy and matter

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

Gómez-Valent, Adrià; Karimkhani, Elahe; Solà, Joan, E-mail: adriagova@ecm.ub.edu, E-mail: e.karimkhani91@basu.ac.ir, E-mail: sola@ecm.ub.edu

We determine the Hubble expansion and the general cosmic perturbation equations for a general system consisting of self-conserved matter, ρ{sub m}, and self-conserved dark energy (DE), ρ{sub D}. While at the background level the two components are non-interacting, they do interact at the perturbations level. We show that the coupled system of matter and DE perturbations can be transformed into a single, third order, matter perturbation equation, which reduces to the (derivative of the) standard one in the case that the DE is just a cosmological constant. As a nontrivial application we analyze a class of dynamical models whose DEmore » density ρ{sub D}(H) consists of a constant term, C{sub 0}, and a series of powers of the Hubble rate. These models were previously analyzed from the point of view of dynamical vacuum models, but here we treat them as self-conserved DE models with a dynamical equation of state. We fit them to the wealth of expansion history and linear structure formation data and compare their fit quality with that of the concordance ΛCDM model. Those with C{sub 0}=0 include the so-called ''entropic-force'' and ''QCD-ghost'' DE models, as well as the pure linear model ρ{sub D}∼H, all of which appear strongly disfavored. The models with C{sub 0}≠0 , in contrast, emerge as promising dynamical DE candidates whose phenomenological performance is highly competitive with the rigid Λ-term inherent to the ΛCDM.« less

Entrainment of bed material by Earth-surface mass flows: review and reformulation of depth-integrated theory

USGS Publications Warehouse

Iverson, Richard M.; Chaojun Ouyang,

2015-01-01

Earth-surface mass flows such as debris flows, rock avalanches, and dam-break floods can grow greatly in size and destructive potential by entraining bed material they encounter. Increasing use of depth-integrated mass- and momentum-conservation equations to model these erosive flows motivates a review of the underlying theory. Our review indicates that many existing models apply depth-integrated conservation principles incorrectly, leading to spurious inferences about the role of mass and momentum exchanges at flow-bed boundaries. Model discrepancies can be rectified by analyzing conservation of mass and momentum in a two-layer system consisting of a moving upper layer and static lower layer. Our analysis shows that erosion or deposition rates at the interface between layers must in general satisfy three jump conditions. These conditions impose constraints on valid erosion formulas, and they help determine the correct forms of depth-integrated conservation equations. Two of the three jump conditions are closely analogous to Rankine-Hugoniot conditions that describe the behavior of shocks in compressible gasses, and the third jump condition describes shear traction discontinuities that necessarily exist across eroding boundaries. Grain-fluid mixtures commonly behave as compressible materials as they undergo entrainment, because changes in bulk density occur as the mixtures mobilize and merge with an overriding flow. If no bulk density change occurs, then only the shear-traction jump condition applies. Even for this special case, however, accurate formulation of depth-integrated momentum equations requires a clear distinction between boundary shear tractions that exist in the presence or absence of bed erosion.

Helicity and other conservation laws in perfect fluid motion

NASA Astrophysics Data System (ADS)

Serre, Denis

2018-03-01

In this review paper, we discuss helicity from a geometrical point of view and see how it applies to the motion of a perfect fluid. We discuss its relation with the Hamiltonian structure, and then its extension to arbitrary space dimensions. We also comment about the existence of additional conservation laws for the Euler equation, and its unlikely integrability in Liouville's sense.

Stabilised finite-element methods for solving the level set equation with mass conservation

NASA Astrophysics Data System (ADS)

Kabirou Touré, Mamadou; Fahsi, Adil; Soulaïmani, Azzeddine

2016-01-01

Finite-element methods are studied for solving moving interface flow problems using the level set approach and a stabilised variational formulation proposed in Touré and Soulaïmani (2012; Touré and Soulaïmani To appear in 2016), coupled with a level set correction method. The level set correction is intended to enhance the mass conservation satisfaction property. The stabilised variational formulation (Touré and Soulaïmani 2012; Touré and Soulaïmani, To appear in 2016) constrains the level set function to remain close to the signed distance function, while the mass conservation is a correction step which enforces the mass balance. The eXtended finite-element method (XFEM) is used to take into account the discontinuities of the properties within an element. XFEM is applied to solve the Navier-Stokes equations for two-phase flows. The numerical methods are numerically evaluated on several test cases such as time-reversed vortex flow, a rigid-body rotation of Zalesak's disc, sloshing flow in a tank, a dam-break over a bed, and a rising bubble subjected to buoyancy. The numerical results show the importance of satisfying global mass conservation to accurately capture the interface position.

Numerical simulation of conservation laws

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; To, Wai-Ming

1992-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

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

Waluga, Christian, E-mail: waluga@ma.tum.de; Wohlmuth, Barbara; Rüde, Ulrich

2016-01-15

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilizedmore » linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.« less

Relativistic Newtonian dynamics

NASA Astrophysics Data System (ADS)

Friedman, Yaakov; Mendel Steiner, Joseph

2017-05-01

A new Relativistic Newtonian Dynamics (RND) for motion under a conservative force capable to describe non-classical behavior in astronomy is proposed. The rotor experiments using Mössbauer spectroscopy with synchrotron radiation, described in the paper, indicate the influence of non-gravitational acceleration or potential energy on time. Similarly, the observed precession of Mercury and the periastron advance of binaries can be explained by the influence of gravitational potential energy on spacetime. The proposed RND incorporates the influence of potential energy on spacetime in Newton’s dynamics. The effect of this influence on time intervals, space increments and velocities is described explicitly by the use of the concept of escape trajectory. For an attracting conservative static potential we derived the RND energy conservation and the dynamics equation for motion of objects with non-zero mass and for massless particles. These equations are subsequently simplified for motion under a central force. Without the need to curve spacetime, this model predicts accurately the four non-classical observations in astronomy used to test the General Relativity.

On inter-tidal transport equation

USGS Publications Warehouse

Cheng, Ralph T.; Feng, Shizuo; Pangen, Xi

1989-01-01

The transports of solutes, sediments, nutrients, and other tracers are fundamental to the interactive physical, chemical, and biological processes in estuaries. The characteristic time scales for most estuarine biological and chemical processes are on the order of several tidal cycles or longer. To address the long-term transport mechanism meaningfully, the formulation of an inter-tidal conservation equation is the main subject of this paper. The commonly used inter-tidal conservation equation takes the form of a convection-dispersion equation in which the convection is represented by the Eulerian residual current, and the dispersion terms are due to the introduction of a Fickian hypothesis, unfortunately, the physical significance of this equation is not clear, and the introduction of a Fickian hypothesis is at best an ad hoc approximation. Some recent research results on the Lagrangian residual current suggest that the long-term transport problem is more closely related to the Lagrangian residual current than to the Eulerian residual current. With the aid of additional insight of residual current, the inter-tidal transport equation has been reformulated in this paper using a small perturbation method for a weakly nonlinear tidal system. When tidal flows can be represented by an M2 system, the new intertidal transport equation also takes the form of a convective-dispersion equation without the introduction of a Fickian hypothesis. The convective velocity turns out to be the first order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes’ drift), and the correlation terms take the form of convection with the Stokes’ drift as the convective velocity. The remaining dispersion terms are perturbations of lower order solution to higher order solutions due to shear effect and turbulent mixing.

General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks

NASA Astrophysics Data System (ADS)

Donmez, Orhan

We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.

Controlling Wavebreaking in a Viscous Fluid Conduit

NASA Astrophysics Data System (ADS)

Anderson, Dalton; Maiden, Michelle; Hoefer, Mark

2015-11-01

This poster will present a new technique in the experimental investigation of dispersive hydrodynamics. In shallow water flows, internal ocean waves, superfluids, and optical media, wave breaking can be resolved by a dispersive shock wave (DSW). In this work, an experimental method to control the location of DSW formation (gradient catastrophe) is explained. The central idea is to convert an initial value problem (Riemann problem) into an equivalent boundary value problem. The system to which this technique is applied is a fluid conduit resulting from high viscosity contrast between a buoyant interior and heavier exterior fluid. The conduit cross-sectional area is modeled by a nonlinear, conservative, dispersive, third order partial differential equation. Using this model, the aim is to predict the breaking location of a DSW by controlling one boundary condition. An analytical expression for this boundary condition is derived by solving the dispersionless equation backward in time from the desired step via the method of characteristics. This is used in experiment to generate an injection rate profile for a high precision piston pump. This translates to the desired conduit shape. Varying the jump height and desired breaking location indicates good control of DSW formation. This result can be improved by deriving a conduit profile by numerical simulation of the full model equation. Controlling the breaking location of a DSW allows for the investigation of dynamics independent of the boundary. Support provided by NSF CAREER DMS-1255422 , NSF EXTREEMS.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations

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

Schüler, D.; Alonso, S.; Bär, M.

2014-12-15

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexistingmore » static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.« less

Simulation of mixing in the quick quench region of a rich burn-quick quench mix-lean burn combustor

NASA Technical Reports Server (NTRS)

Shih, Tom I.-P.; Nguyen, H. Lee; Howe, Gregory W.; Li, Z.

1991-01-01

A computer program was developed to study the mixing process in the quick quench region of a rich burn-quick quench mix-lean burn combustor. The computer program developed was based on the density-weighted, ensemble-averaged conservation equations of mass, momentum (full compressible Navier-Stokes), total energy, and species, closed by a k-epsilon turbulence model with wall functions. The combustion process was modeled by a two-step global reaction mechanism, and NO(x) formation was modeled by the Zeldovich mechanism. The formulation employed in the computer program and the essence of the numerical method of solution are described. Some results obtained for nonreacting and reacting flows with different main-flow to dilution-jet momentum flux ratios are also presented.

Overview of Edge Simulation Laboratory (ESL)

NASA Astrophysics Data System (ADS)

Cohen, R. H.; Dorr, M.; Hittinger, J.; Rognlien, T.; Umansky, M.; Xiong, A.; Xu, X.; Belli, E.; Candy, J.; Snyder, P.; Colella, P.; Martin, D.; Sternberg, T.; van Straalen, B.; Bodi, K.; Krasheninnikov, S.

2006-10-01

The ESL is a new collaboration to build a full-f electromagnetic gyrokinetic code for tokamak edge plasmas using continuum methods. Target applications are edge turbulence and transport (neoclassical and anomalous), and edge-localized modes. Initially the project has three major threads: (i) verification and validation of TEMPEST, the project's initial (electrostatic) edge code which can be run in 4D (neoclassical and transport-timescale applications) or 5D (turbulence); (ii) design of the next generation code, which will include more complete physics (electromagnetics, fluid equation option, improved collisions) and advanced numerics (fully conservative, high-order discretization, mapped multiblock grids, adaptivity), and (iii) rapid-prototype codes to explore the issues attached to solving fully nonlinear gyrokinetics with steep radial gradiens. We present a brief summary of the status of each of these activities.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

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

Gerritsma, Marc; Bochev, Pavel

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Discontinuous Galerkin Methods for NonLinear Differential Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy; Mansour, Nagi (Technical Monitor)

2001-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Audible thunder characteristic and the relation between peak frequency and lightning parameters

NASA Astrophysics Data System (ADS)

Yuhua, Ouyang; Ping, Yuan

2012-02-01

In recent summers, some natural lightning optical spectra and audible thunder signals were observed. Twelve events on 15 August 2008 are selected as samples since some synchronizing information about them are obtained, such as lightning optical spectra, surface E-field changes, etc. By using digital filter and Fourier transform, thunder frequency spectra in observation location have been calculated. Then the two main propagation effects, finite amplitude propagation and attenuation by air, are calculated. Upon that we take the test thunder frequency spectra and work backward to recalculate the original frequency spectra near generation location. Thunder frequency spectra and the frequency distribution varying with distance are researched. According to the theories on plasma, the channel temperature and electron density are further calculated by transition parameters of lines in lightning optical spectra. Pressure and the average ionization degree of each discharge channel are obtained by using Saha equations, charge conservation equations and particle conservation equations. Moreover, the relationship between the peak frequency of each thunder and channel parameters of the lightning is studied.

Multi criteria evaluation for universal soil loss equation based on geographic information system

NASA Astrophysics Data System (ADS)

Purwaamijaya, I. M.

2018-05-01

The purpose of this research were to produce(l) a conceptual, functional model designed and implementation for universal soil loss equation (usle), (2) standard operational procedure for multi criteria evaluation of universal soil loss equation (usle) using geographic information system, (3) overlay land cover, slope, soil and rain fall layers to gain universal soil loss equation (usle) using multi criteria evaluation, (4) thematic map of universal soil loss equation (usle) in watershed, (5) attribute table of universal soil loss equation (usle) in watershed. Descriptive and formal correlation methods are used for this research. Cikapundung Watershed, Bandung, West Java, Indonesia was study location. This research was conducted on January 2016 to May 2016. A spatial analysis is used to superimposed land cover, slope, soil and rain layers become universal soil loss equation (usle). Multi criteria evaluation for universal soil loss equation (usle) using geographic information system could be used for conservation program.

A new two-metric theory of gravity with prior geometry

NASA Technical Reports Server (NTRS)

Lightman, A. P.; Lee, D. L.

1972-01-01

A theory is presented of gravity which has the same post-Newtonian (PN) as that of general relativity. The field equations, and a calculation of the PN limit of the theory are discussed along with the equations of stellar structure for static spherically symmetric stars. A special exterior spherically symmetric solution, time dependent solutions, conservations, and gravitational waves are analyzed.

Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the Boltzmann equation

NASA Astrophysics Data System (ADS)

Molnár, E.; Niemi, H.; Rischke, D. H.

2016-12-01

In Molnár et al. Phys. Rev. D 93, 114025 (2016) the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-particle distribution function. In this paper we make a particular choice for this distribution function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.

Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence

NASA Astrophysics Data System (ADS)

Hahm, T. S.; Wang, Lu; Madsen, J.

2009-02-01

An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E ×B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov-Maxwell system. Generalized ordering takes ρi≪ρθi˜LE˜Lp≪R [here ρi is the thermal ion Larmor radius and ρθi=B /(Bθρi)], as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. k⊥ρi˜1 is assumed for generality, and the relative fluctuation amplitudes eδϕ /Ti˜δB/B are kept up to the second order. Extending the electrostatic theory in the presence of high E ×B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pullback transformation from the gyrocenter distribution function in the gyrokinetic Maxwell's equation.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

Reconstruction of Twist Torque in Main Parachute Risers

NASA Technical Reports Server (NTRS)

Day, Joshua D.

2015-01-01

The reconstruction of twist torque in the Main Parachute Risers of the Capsule Parachute Assembly System (CPAS) has been successfully used to validate CPAS Model Memo conservative twist torque equations. Reconstruction of basic, one degree of freedom drop tests was used to create a functional process for the evaluation of more complex, rigid body simulation. The roll, pitch, and yaw of the body, the fly-out angles of the parachutes, and the relative location of the parachutes to the body are inputs to the torque simulation. The data collected by the Inertial Measurement Unit (IMU) was used to calculate the true torque. The simulation then used photogrammetric and IMU data as inputs into the Model Memo equations. The results were then compared to the true torque results to validate the Model Memo equations. The Model Memo parameters were based off of steel risers and the parameters will need to be re-evaluated for different materials. Photogrammetric data was found to be more accurate than the inertial data in accounting for the relative rotation between payload and cluster. The Model Memo equations were generally a good match and when not matching were generally conservative.

Flowfield computation of entry vehicles

NASA Technical Reports Server (NTRS)

Prabhu, Dinesh K.

1990-01-01

The equations governing the multidimensional flow of a reacting mixture of thermally perfect gasses were derived. The modeling procedures for the various terms of the conservation laws are discussed. A numerical algorithm, based on the finite-volume approach, to solve these conservation equations was developed. The advantages and disadvantages of the present numerical scheme are discussed from the point of view of accuracy, computer time, and memory requirements. A simple one-dimensional model problem was solved to prove the feasibility and accuracy of the algorithm. A computer code implementing the above algorithm was developed and is presently being applied to simple geometries and conditions. Once the code is completely debugged and validated, it will be used to compute the complete unsteady flow field around the Aeroassist Flight Experiment (AFE) body.

Relativistic electromagnetic waves in an electron-ion plasma

NASA Technical Reports Server (NTRS)

Chian, Abraham C.-L.; Kennel, Charles F.

1987-01-01

High power laser beams can drive plasma particles to relativistic energies. An accurate description of strong waves requires the inclusion of ion dynamics in the analysis. The equations governing the propagation of relativistic electromagnetic waves in a cold electron-ion plasma can be reduced to two equations expressing conservation of energy-momentum of the system. The two conservation constants are functions of the plasma stream velocity, the wave velocity, the wave amplitude, and the electron-ion mass ratio. The dynamic parameter, expressing electron-ion momentum conversation in the laboratory frame, can be regarded as an adjustable quantity, a suitable choice of which will yield self-consistent solutions when other plasma parameters were specified. Circularly polarized electromagnetic waves and electrostatic plasma waves are used as illustrations.

On locally and nonlocally related potential systems

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.; Bluman, George W.

2010-07-01

For any partial differential equation (PDE) system, a local conservation law yields potential equations in terms of some potential variable, which normally is a nonlocal variable. The current paper examines situations when such a potential variable is a local variable, i.e., is a function of the independent and dependent variables of a given PDE system, and their derivatives. In the case of two independent variables, a simple necessary and sufficient condition is presented for the locality of such a potential variable, and this is illustrated by several examples. As a particular example, two-dimensional reductions of equilibrium equations for fluid and plasma dynamics are considered. It is shown that such reductions with respect to helical, axial, and translational symmetries have conservation laws which yield local potential variables. This leads to showing that the well-known Johnson-Frieman-Kruskal-Oberman (JFKO) and Bragg-Hawthorne (Grad-Shafranov) equations are locally related to the corresponding helically and axially symmetric PDE systems of fluid/plasma dynamics. For the axially symmetric case, local symmetry classifications and arising invariant solutions are compared for the original PDE system and the Bragg-Hawthorne (potential) equation. The potential equation is shown to have additional symmetries, denoted as restricted symmetries. Restricted symmetries leave invariant a family of solutions of a given PDE system but not the whole solution manifold, and hence are not symmetries of the given PDE system. Corresponding reductions are shown to yield solutions, which are not obtained as invariant solutions from local symmetry reduction.

Test-particle motion in the nonsymmetric gravitation theory

NASA Astrophysics Data System (ADS)

Moffat, J. W.

1987-06-01

A derivation of the motion of test particles in the nonsymmetric gravitational theory (NGT) is given using the field equations in the presence of matter. The motion of the particle is governed by the Christoffel symbols, which are formed from the symmetric part of the fundamental tensor gμν, as well as by a tensorial piece determined by the skew part of the contracted curvature tensor Rμν. Given the energy-momentum tensor for a perfect fluid and the definition of a test particle in the NGT, the equations of motion follow from the conservation laws. The tensorial piece in the equations of motion describes a new force in nature that acts on the conserved charge in a body. Particles that carry this new charge do not follow geodesic world lines in the NGT, whereas photons do satisfy geodesic equations of motion and the equivalence principle of general relativity. Astronomical predictions, based on the exact static, spherically symmetric solution of the field equations in a vacuum and the test-particle equations of motion, are derived in detail. The maximally extended coordinates that remove the event-horizon singularities in the static, spherically symmetric solution are presented. It is shown how an inward radially falling test particle can be prevented from forming an event horizon for a value greater than a specified critical value of the source charge. If a test particle does fall through an event horizon, then it must continue to fall until it reaches the singularity at r=0.

Principles and equations for measuring and interpreting protein stability: From monomer to tetramer.

PubMed

Bedouelle, Hugues

2016-02-01

The ability to measure the thermodynamic stability of proteins with precision is important for both academic and applied research. Such measurements rely on mathematical models of the protein denaturation profile, i.e. the relation between a global protein signal, corresponding to the folding states in equilibrium, and the variable value of a denaturing agent, either heat or a chemical molecule, e.g. urea or guanidinium hydrochloride. In turn, such models rely on a handful of physical laws: the laws of mass action and conservation, the law that relates the protein signal and concentration, and the one that relates stability and denaturant value. So far, equations have been derived mainly for the denaturation profiles of homomeric proteins. Here, we review the underlying basic physical laws and show in detail how to derive model equations for the unfolding equilibria of homomeric or heteromeric proteins up to trimers and potentially tetramers, with or without folding intermediates, and give full demonstrations. We show that such equations cannot be derived for pentamers or higher oligomers except in special degenerate cases. We expand the method to signals that do not correspond to extensive protein properties. We review and expand methods for uncovering hidden intermediates of unfolding. Finally, we review methods for comparing and interpreting the thermodynamic parameters that derive from stability measurements for cognate wild-type and mutant proteins. This work should provide a robust theoretical basis for measuring the stability of complex proteins. Copyright © 2015 Elsevier B.V. and Société Française de Biochimie et Biologie Moléculaire (SFBBM). All rights reserved.

Development and Application of Compatible Discretizations of Maxwell's Equations

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

White, D; Koning, J; Rieben, R

We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we havemore » designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve.« less

Compatible, total energy conserving and symmetry preserving arbitrary Lagrangian-Eulerian hydrodynamics in 2D rz - Cylindrical coordinates

NASA Astrophysics Data System (ADS)

Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail

2014-07-01

We present a new discretization for 2D arbitrary Lagrangian-Eulerian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic Lagrangian hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the Lagrangian equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its “Cartesian” form with a special definition of “planar” masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of “planar” subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; formulated for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for Lagrangian equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary Lagrangian-Eulerian algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a local constrained-optimization-based approach for each zone to find the subzonal mass fluxes. In this paper we give a systematic and complete description of the algorithm for the axisymmetric case and provide justification for our approach. The ALE algorithm conserves total energy on arbitrary meshes and preserves symmetry when remapping from one equiangular polar mesh to another. The principal contributions of this part of the paper are the extension of this algorithm to general polygonal meshes and 2D rz geometry with requirement of symmetry preservation on special meshes. We present numerical examples that demonstrate the robustness of the new ALE method on a variety of grids and test problems including polygonal meshes and some realistic experiments. We confirm the importance of conservation of total energy for correctly modeling shock waves.

A family of wave equations with some remarkable properties.

PubMed

da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos

2018-02-01

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.

Effects of zonal flows on correlation between energy balance and energy conservation associated with nonlinear nonviscous atmospheric dynamics in a thin rotating spherical shell

NASA Astrophysics Data System (ADS)

Ibragimov, Ranis N.

2018-03-01

The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

Some special solutions to the Hyperbolic NLS equation

NASA Astrophysics Data System (ADS)

Vuillon, Laurent; Dutykh, Denys; Fedele, Francesco

2018-04-01

The Hyperbolic Nonlinear SCHRöDINGER equation (HypNLS) arises as a model for the dynamics of three-dimensional narrow-band deep water gravity waves. In this study, the symmetries and conservation laws of this equation are computed. The PETVIASHVILI method is then exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly accurate FOURIER solver.

A quasi-steady state cosmological model with creation of matter

NASA Technical Reports Server (NTRS)

Hoyle, F.; Burbidge, G.; Narlikar, J. V.

1993-01-01

A universe is envisioned in which there was a major creation episode when the mean universal density was about 10 to the -27 g/cu cm. Explicit equations are given for the creation of matter; in a cosmological approximation, these equations lead to expressions for the time-dependence of the cosmological scale factor S(t), but do not entail, as big bang cosmology does, that S(t) tend to zero at some finite time t. The equations therefore possess a universality that is absent from big bang cosmology. Creation occurs when certain conservation equations involving the gradient of a scalar field C(i) are satisfied.

Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential

NASA Technical Reports Server (NTRS)

Campbell, Joel

2009-01-01

The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1995-01-01

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

A coupled-oscillator model with a conservation law for the rhythmic amoeboid movements of plasmodial slime molds

NASA Astrophysics Data System (ADS)

Tero, A.; Kobayashi, R.; Nakagaki, T.

2005-06-01

Experiments on the fusion and partial separation of plasmodia of the true slime mold Physarum polycephalum are described, concentrating on the spatio-temporal phase patterns of rhythmic amoeboid movement. On the basis of these experimental results we introduce a new model of coupled oscillators with one conserved quantity. Simulations using the model equations reproduce the experimental results well.

Parallel CE/SE Computations via Domain Decomposition

NASA Technical Reports Server (NTRS)

Himansu, Ananda; Jorgenson, Philip C. E.; Wang, Xiao-Yen; Chang, Sin-Chung

2000-01-01

This paper describes the parallelization strategy and achieved parallel efficiency of an explicit time-marching algorithm for solving conservation laws. The Space-Time Conservation Element and Solution Element (CE/SE) algorithm for solving the 2D and 3D Euler equations is parallelized with the aid of domain decomposition. The parallel efficiency of the resultant algorithm on a Silicon Graphics Origin 2000 parallel computer is checked.

A new stream function formulation for the Euler equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Hassan, H. A.

1983-01-01

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

Action principle for Coulomb collisions in plasmas

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

Hirvijoki, Eero

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

GFSSP Training Course Lectures

NASA Technical Reports Server (NTRS)

Majumdar, Alok K.

2008-01-01

GFSSP has been extended to model conjugate heat transfer Fluid Solid Network Elements include: a) Fluid nodes and Flow Branches; b) Solid Nodes and Ambient Nodes; c) Conductors connecting Fluid-Solid, Solid-Solid and Solid-Ambient Nodes. Heat Conduction Equations are solved simultaneously with Fluid Conservation Equations for Mass, Momentum, Energy and Equation of State. The extended code was verified by comparing with analytical solution for simple conduction-convection problem The code was applied to model: a) Pressurization of Cryogenic Tank; b) Freezing and Thawing of Metal; c) Chilldown of Cryogenic Transfer Line; d) Boil-off from Cryogenic Tank.

Action principle for Coulomb collisions in plasmas

DOE PAGES

Hirvijoki, Eero

2016-09-14

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

On a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation

NASA Astrophysics Data System (ADS)

Zhao, Hai-qiong

2017-02-01

In this paper, a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation is investigated. The underlying integrable structures like the Lax pair, the infinite number of conservation laws, the Darboux-Bäcklund transformation, and the solutions are presented in the explicit form. The theory of the semi-discrete equation including integrable properties yields the corresponding theory of the continuous counterpart in the continuous limit. Finally, numerical experiments are provided to demonstrate the effectiveness of the developed integrable semi-discretization algorithms.

Allometric equations for estimating tree biomass in restored mixed-species Atlantic Forest stands

Treesearch

Lauro Rodrigues Nogueira; Vera Lex Engel; John A. Parrotta; Antonio Carlos Galvão de Melo; Danilo Scorzoni Ré

2014-01-01

Restoration of Atlantic Forests is receiving increasing attention because of its role in both biodiversity conservation and carbon sequestration for global climate change mitigation. This study was carried out in an Atlantic Forest restoration project in the south-central region of São Paulo State – Brazil to develop allometric equations to estimate tree biomass of...

Classical-Quantum Correspondence by Means of Probability Densities

NASA Technical Reports Server (NTRS)

Vegas, Gabino Torres; Morales-Guzman, J. D.

1996-01-01

Within the frame of the recently introduced phase space representation of non relativistic quantum mechanics, we propose a Lagrangian from which the phase space Schrodinger equation can be derived. From that Lagrangian, the associated conservation equations, according to Noether's theorem, are obtained. This shows that one can analyze quantum systems completely in phase space as it is done in coordinate space, without additional complications.

A coupled implicit method for chemical non-equilibrium flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun; Chen, Kuo-Huey; Choi, Yunho

1993-01-01

The present time-accurate coupled-solution procedure addresses the chemical nonequilibrium Navier-Stokes equations over a wide Mach-number range uses, in conjunction with the strong conservation form of the governing equations, five unknown primitive variables. The numerical tests undertaken address steady convergent-divergent nozzle flows with air dissociation/recombination, dump combustor flows with n-pentane/air chemistry, and unsteady nonreacting cavity flows.

Numerical investigation of sixth order Boussinesq equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.; Vucheva, V.

2017-10-01

We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.

Flux Jacobian Matrices For Equilibrium Real Gases

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1990-01-01

Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.

A tensor formulation of the equation of transfer for spherically symmetric flows. [radiative transfer in seven dimensional Riemannian space

NASA Technical Reports Server (NTRS)

Haisch, B. M.

1976-01-01

A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

A quasi-3D wire approach to model pulmonary airflow in human airways.

PubMed

Kannan, Ravishekar; Chen, Z J; Singh, Narender; Przekwas, Andrzej; Delvadia, Renishkumar; Tian, Geng; Walenga, Ross

2017-07-01

The models used for modeling the airflow in the human airways are either 0-dimensional compartmental or full 3-dimensional (3D) computational fluid dynamics (CFD) models. In the former, airways are treated as compartments, and the computations are performed with several assumptions, thereby generating a low-fidelity solution. The CFD method displays extremely high fidelity since the solution is obtained by solving the conservation equations in a physiologically consistent geometry. However, CFD models (1) require millions of degrees of freedom to accurately describe the geometry and to reduce the discretization errors, (2) have convergence problems, and (3) require several days to simulate a few breathing cycles. In this paper, we present a novel, fast-running, and robust quasi-3D wire model for modeling the airflow in the human lung airway. The wire mesh is obtained by contracting the high-fidelity lung airway surface mesh to a system of connected wires, with well-defined radii. The conservation equations are then solved in each wire. These wire meshes have around O(1000) degrees of freedom and hence are 3000 to 25 000 times faster than their CFD counterparts. The 3D spatial nature is also preserved since these wires are contracted out of the actual lung STL surface. The pressure readings between the 2 approaches showed minor difference (maximum error = 15%). In general, this formulation is fast and robust, allows geometric changes, and delivers high-fidelity solutions. Hence, this approach has great potential for more complicated problems including modeling of constricted/diseased lung sections and for calibrating the lung flow resistances through parameter inversion. Copyright © 2016 John Wiley & Sons, Ltd.

On the classification of scalar evolution equations with non-constant separant

NASA Astrophysics Data System (ADS)

Hümeyra Bilge, Ayşe; Mizrahi, Eti

2017-01-01

The ‘separant’ of the evolution equation u t   =  F, where F is some differentiable function of the derivatives of u up to order m, is the partial derivative \\partial F/\\partial {{u}m}, where {{u}m}={{\\partial}m}u/\\partial {{x}m} . As an integrability test, we use the formal symmetry method of Mikhailov-Shabat-Sokolov, which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives a sequence of conservation laws, called the ‘conserved densities’ {ρ(i)}, i=-1,1,2,3,\\ldots . We apply this method to the classification of scalar evolution equations of orders 3≤slant m≤slant 15 , for which {ρ(-1)}={≤ft[\\partial F/\\partial {{u}m}\\right]}-1/m} and {{ρ(1)} are non-trivial, i.e. they are not total derivatives and {ρ(-1)} is not linear in its highest order derivative. We obtain the ‘top level’ parts of these equations and their ‘top dependencies’ with respect to the ‘level grading’, that we defined in a previous paper, as a grading on the algebra of polynomials generated by the derivatives u b+i , over the ring of {{C}∞} functions of u,{{u}1},\\ldots,{{u}b} . In this setting b and i are called ‘base’ and ‘level’, respectively. We solve the conserved density conditions to show that if {ρ(-1)} depends on u,{{u}1},\\ldots,{{u}b}, then, these equations are level homogeneous polynomials in {{u}b+i},\\ldots,{{u}m} , i≥slant 1 . Furthermore, we prove that if {ρ(3)} is non-trivial, then {ρ(-1)}={≤ft(α ub2+β {{u}b}+γ \\right)}1/2} , with b≤slant 3 while if {{ρ(3)} is trivial, then {ρ(-1)}={≤ft(λ {{u}b}+μ \\right)}1/3} , where b≤slant 5 and α, β, γ, λ and μ are functions of u,\\ldots,{{u}b-1} . We show that the equations that we obtain form commuting flows and we construct their recursion operators that are respectively of orders 2 and 6 for non-trivial and trivial {{ρ(3)} respectively. Omitting lower order dependencies, we show that equations with non-trivial {ρ(3)} and b  =  3 are symmetries of the ‘essentially non-linear third order equation’ for trivial {ρ(3)} , the equations with b  =  5 are symmetries of a non-quasilinear fifth order equation obtained in previous work, while for b  =  3, 4 they are symmetries of quasilinear fifth order equations.

Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states

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

Gamba, Irene M.; Tharkabhushanam, Sri Harsha

We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S{sup d-1}. The conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibilitymore » (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: ()]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M. Ernst, Velocity distributions in homogeneously cooling and heated granular fluids, Granular Matter 1(57) (1998); M.H. Ernst, R. Brito, Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails, Journal of Statistical Physics 109 (2002) 407-432; S.J. Moon, M.D. Shattuck, J. Swift, Velocity distributions and correlations in homogeneously heated granular media, Physical Review E 64 (2001) 031303; I.M. Gamba, S. Rjasanow, W. Wagner, Direct simulation of the uniformly heated granular Boltzmann equation, Mathematical and Computer Modelling 42 (2005) 683-700] and rigorously proven in Gamba et al. [I.M. Gamba, V. Panferov, C. Villani, On the Boltzmann equation for diffusively excited granular media, Communications in Mathematical Physics 246 (2004) 503-541(39)] and [A.V. Bobylev, I.M. Gamba, V. Panferov, Moment inequalities and high-energy tails for Boltzmann equations with inelastic interactions, Journal of Statistical Physics 116 (2004) 1651-1682].« less

Combustion of liquid-fuel droplets in supercritical conditions

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Yang, Vigor; Hsaio, C. C.

1992-01-01

A comprehensive analysis of liquid-fuel droplet combustion in both subcritical and supercritical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates variable thermophysical properties, finite-rate chemical kinetics, and a full treatment of liquid-vapor phase equilibrium at the drop surface. The governing equations and associated interfacial boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures in the range of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influence on fluid transport, gas-liquid interfacial thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibit a considerable change in the combustion mechanism at the critical pressure, mainly as a result of reduced mass diffusivity and latent heat of vaporization with increased pressure.

Black holes in six-dimensional conformal gravity

NASA Astrophysics Data System (ADS)

Lü, H.; Pang, Yi; Pope, C. N.

2013-05-01

We study conformally invariant theories of gravity in six dimensions. In four dimensions, there is a unique such theory that is polynomial in the curvature and its derivatives, namely, Weyl-squared, and furthermore all solutions of Einstein gravity are also solutions of the conformal theory. By contrast, in six dimensions there are three independent conformally invariant polynomial terms one could consider. There is a unique linear combination (up to overall scale) for which Einstein metrics are also solutions, and this specific theory forms the focus of our attention in this paper. We reduce the equations of motion for the most general spherically symmetric black hole to a single fifth-order differential equation. We obtain the general solution in the form of an infinite series, characterized by five independent parameters, and we show how a finite three-parameter truncation reduces to the already known Schwarzschild-AdS metric and its conformal scaling. We derive general results for the thermodynamics and the first law for the full five-parameter solutions. We also investigate solutions in extended theories coupled to conformally invariant matter, and in addition we derive some general results for conserved charges in cubic-curvature theories in arbitrary dimensions.

Combustion of liquid fuel droplets in supercritical conditions

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Yang, Vigor

1991-01-01

A comprehensive analysis of liquid-fuel droplet combustion in both sub- and super-critical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates finite-rate chemical kinetics and a full treatment of liquid-vapor phase equilibrium at the droplet surface. The governing equations and the associated interface boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to the supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influences on the fluid transport, gas/liquid interface thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibits a significant variation near the critical burning pressure, mainly as a result of reduced mass-diffusion rate and latent heat of vaporization with increased pressure. The influence of droplet size on the burning characteristics is also noted.

Numerical Simulations of High-Speed Chemically Reacting Flow

NASA Technical Reports Server (NTRS)

Ton, V. T.; Karagozian, A. R.; Marble, F. E.; Osher, S. J.; Engquist, B. E.

1994-01-01

The essentially nonoscillatory (ENO) shock-capturing scheme for the solution of hyperbolic equations is extended to solve a system of coupled conservation equations governing two-dimensional, time-dependent, compressible chemically reacting flow with full chemistry. The thermodynamic properties of the mixture are modeled accurately, and stiff kinetic terms are separated from the fluid motion by a fractional step algorithm. The methodology is used to study the concept of shock-induced mixing and combustion, a process by which the interaction of a shock wave with a jet of low-density hydrogen fuel enhances mixing through streamwise vorticity generation. Test cases with and without chemical reaction are explored here. Our results indicate that, in the temperature range examined, vorticity generation as well as the distribution of atomic species do not change significantly with the introduction of a chemical reaction and subsequent heat release. The actual diffusion of hydrogen is also relatively unaffected by the reaction process. This suggests that the fluid mechanics of this problem may be successfully decoupled from the combustion processes, and that computation of the mixing problem (without combustion chemistry) can elucidate much of the important physical features of the flow.

Numerical Simulations of High-Speed Chemically Reacting Flow

NASA Technical Reports Server (NTRS)

Ton, V. T.; Karagozin, A. R.; Marble, F. E.; Osher, S. J.; Engquist, B. E.

1994-01-01

The Essentially NonOscillatory (ENO) shock-capturing scheme for the solution of hyperbolic equations is extended to solve a system of coupled conservation equations governing two-dimensional, time-dependent, compressible chemically reacting flow with full chemistry. The thermodynamic properties of the mixture are modeled accurately, and stiff kinetic terms are separated from the fluid motion by a fractional step algorithm. The methodology is used to study the concept of shock-induced mixing and combustion, a process by which the interaction of a shock wave with a jet of low-density hydrogen fuel enhances mixing through streamwise vorticity generation. Test cases with and without chemical reaction are explored here. Our results indicate that, in the temperature range examined, vorticity generation as well as the distribution of atomic species do not change significantly with the introduction of a chemical reaction and subsequent heat release. The actual diffusion of hydrogen is also relatively unaffected by the reaction process. This suggests that the fluid mechanics of this problem may be successfully decoupled from the combustion processes, and that computation of the mixing problem (without combustion chemistry) can elucidate much of the important physical features of the flow.

Numerical simulation of supersonic water vapor jet impinging on a flat plate

NASA Astrophysics Data System (ADS)

Kuzuu, Kazuto; Aono, Junya; Shima, Eiji

2012-11-01

We investigated supersonic water vapor jet impinging on a flat plate through numerical simulation. This simulation is for estimating heating effect of a reusable sounding rocket during vertical landing. The jet from the rocket bottom is supersonic, M=2 to 3, high temperature, T=2000K, and over-expanded. Atmospheric condition is a stationary standard air. The simulation is base on the full Navier-Stokes equations, and the flow is numerically solved by an unstructured compressible flow solver, in-house code LS-FLOW-RG. In this solver, the transport properties of muti-species gas and mass conservation equations of those species are considered. We employed DDES method as a turbulence model. For verification and validation, we also carried out a simulation under the condition of air, and compared with the experimental data. Agreement between our results and the experimental data are satisfactory. Through this simulation, we calculated the flow under some exit pressure conditions, and discuss the effects of pressure ratio on flow structures, heat transfer and so on. Furthermore, we also investigated diffusion effects of water vapor, and we confirmed that these phenomena are generated by the interaction of atmospheric air and affects the heat transfer to the surrounding environment.

Fast Evaporation of Spreading Droplets of Colloidal Suspensions

NASA Astrophysics Data System (ADS)

Maki, Kara; Kumar, Satish

2011-11-01

When a coffee droplet dries on a countertop, a dark ring of coffee solute is left behind, a phenomenon often referred to as ``the coffee-ring effect.'' A closely related yet less-well-explored phenomenon is the formation of a layer of particles, or skin, at the surface of the droplet. In this work, we explore the behavior of a mathematical model that can qualitatively describe both phenomena. We consider a thin axisymmetric droplet of a colloidal suspension on a horizontal substrate undergoing spreading and rapid evaporation. The lubrication approximation is applied to simplify the mass and momentum conservation equations, and the colloidal particles are allowed to influence droplet rheology through their effect on the viscosity. By describing the transport of the colloidal particles with the full convection-diffusion equation, we are able to capture depthwise gradients in particle concentration and thus describe skin formation, a feature neglected in prior models of droplet evaporation. Whereas capillarity creates a flow that drives particles to the contact line to produce a coffee-ring, Marangoni flows can compete with this and promote skin formation. Increases in viscosity due to particle concentration slow down droplet dynamics, and can lead to a significant reduction in the spreading rate.

Linear Mechanisms and Pressure Fluctuations in Wall Turbulence

NASA Astrophysics Data System (ADS)

Septham, Kamthon; Morrison, Jonathan

2014-11-01

Full-domain, linear feedback control of turbulent channel flow at Reτ <= 400 via vU' at low wavenumbers is an effective method to attenuate turbulent channel flow such that it is relaminarised. The passivity-based control approach is adopted and explained by the conservative characteristics of the nonlinear terms contributing to the Reynolds-Orr equation (Sharma et al .Phys .Fluids 2011). The linear forcing acts on the wall-normal velocity field and thus the pressure field via the linear (rapid) source term of the Poisson equation for pressure fluctuations, 2U'∂v/∂x . The minimum required spanwise wavelength resolution without losing control is constant at λz+ = 125, based on the wall friction velocity at t = 0 . The result shows that the maximum forcing is located at y+ ~ 20 , corresponding to the location of the maximum in the mean-square pressure gradient. The effectiveness of linear control is qualitatively explained by Landahl's theory for timescales, in that the control proceeds via the shear interaction timescale which is much shorter than both the nonlinear and viscous timescales. The response of the rapid (linear) and slow (nonlinear) pressure fluctuations to the linear control is examined and discussed.

Human attitudes towards herpetofauna: The influence of folklore and negative values on the conservation of amphibians and reptiles in Portugal

PubMed Central

2012-01-01

Background Human values and folklore of wildlife strongly influence the effectiveness of conservation efforts. These values and folklore may also vary with certain demographic characteristics such as gender, age, or education. Reptiles and amphibians are among the least appreciated of vertebrates and are victims of many negative values and wrong ideas resulting from the direct interpretation of folklore. We try to demonstrate how these values and folklore can affect the way people relate to them and also the possible conservation impacts on these animals. Methods A questionnaire survey distributed to 514 people in the district of Évora, Portugal, was used to obtain data regarding the hypothesis that the existence of wrong ideas and negative values contributes to the phenomenon of human-associated persecution of these animals. A structural equation model was specified in order to confirm the hypothesis about the possible relationships between the presence of perceptions and negative values about amphibians and reptiles and persecution and anti-conservation attitudes. Sociodemographic variables were also added. Results The results of the model suggest that the presence of folklore and negative values clearly predicts persecution and anti-conservation attitudes towards amphibians and reptiles. Also, the existence of folklore varies sociodemographically, but negative values concerning these animals are widespread in the population. Conclusions With the use of structural equation models, this work is a contribution to the study of how certain ideas and values can directly influence human attitudes towards herpetofauna and how they can be a serious conservation issue. PMID:22316318

Human attitudes towards herpetofauna: the influence of folklore and negative values on the conservation of amphibians and reptiles in Portugal.

PubMed

Ceríaco, Luis Mp

2012-02-08

Human values and folklore of wildlife strongly influence the effectiveness of conservation efforts. These values and folklore may also vary with certain demographic characteristics such as gender, age, or education. Reptiles and amphibians are among the least appreciated of vertebrates and are victims of many negative values and wrong ideas resulting from the direct interpretation of folklore. We try to demonstrate how these values and folklore can affect the way people relate to them and also the possible conservation impacts on these animals. A questionnaire survey distributed to 514 people in the district of Évora, Portugal, was used to obtain data regarding the hypothesis that the existence of wrong ideas and negative values contributes to the phenomenon of human-associated persecution of these animals. A structural equation model was specified in order to confirm the hypothesis about the possible relationships between the presence of perceptions and negative values about amphibians and reptiles and persecution and anti-conservation attitudes. Sociodemographic variables were also added. The results of the model suggest that the presence of folklore and negative values clearly predicts persecution and anti-conservation attitudes towards amphibians and reptiles. Also, the existence of folklore varies sociodemographically, but negative values concerning these animals are widespread in the population. With the use of structural equation models, this work is a contribution to the study of how certain ideas and values can directly influence human attitudes towards herpetofauna and how they can be a serious conservation issue.

A Conserved Current Solid-on-Solid Model on a Sierpinski Tetrahedron Substrate

NASA Astrophysics Data System (ADS)

Kim, Jin Min; Kang, Daeseung

2018-03-01

A conserved current solid-on-solid model with conservative noise on a 3D Sierpinski tetrahedron substrate is studied. The interface width W grows as t β , with β = 0.0396 ± 0.0009, and becomes saturated as L α, with α = 0.195±0.005, where L is the system size. The dynamic exponent z ≈ 4.92 is estimated from the relation z = α/β. These values satisfy a scaling relation α+z = 2z rw , where z rw is the random walk exponent of the fractal substrate. Our results are consistent with the values estimated from a fractional Langevin equation with a conservative noise.

Conservative regularization of compressible dissipationless two-fluid plasmas

NASA Astrophysics Data System (ADS)

Krishnaswami, Govind S.; Sachdev, Sonakshi; Thyagaraja, A.

2018-02-01

This paper extends our earlier approach [cf. A. Thyaharaja, Phys. Plasmas 17, 032503 (2010) and Krishnaswami et al., Phys. Plasmas 23, 022308 (2016)] to obtaining à priori bounds on enstrophy in neutral fluids and ideal magnetohydrodynamics. This results in a far-reaching local, three-dimensional, non-linear, dispersive generalization of a KdV-type regularization to compressible/incompressible dissipationless 2-fluid plasmas and models derived therefrom (quasi-neutral, Hall, and ideal MHD). It involves the introduction of vortical and magnetic "twirl" terms λl 2 ( w l + ( q l / m l ) B ) × ( ∇ × w l ) in the ion/electron velocity equations ( l = i , e ) where w l are vorticities. The cut-off lengths λl and number densities nl must satisfy λl 2 n l = C l , where Cl are constants. A novel feature is that the "flow" current ∑ l q l n l v l in Ampère's law is augmented by a solenoidal "twirl" current ∑ l ∇ × ∇ × λl 2 j flow , l . The resulting equations imply conserved linear and angular momenta and a positive definite swirl energy density E * which includes an enstrophic contribution ∑ l ( 1 / 2 ) λl 2 ρ l wl 2 . It is shown that the equations admit a Hamiltonian-Poisson bracket formulation. Furthermore, singularities in ∇ × B are conservatively regularized by adding ( λB 2 / 2 μ 0 ) ( ∇ × B ) 2 to E * . Finally, it is proved that among regularizations that admit a Hamiltonian formulation and preserve the continuity equations along with the symmetries of the ideal model, the twirl term is unique and minimal in non-linearity and space derivatives of velocities.

Understanding Vector Fields.

ERIC Educational Resources Information Center

Curjel, C. R.

1990-01-01

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

Discrete rational and breather solution in the spatial discrete complex modified Korteweg-de Vries equation and continuous counterparts.

PubMed

Zhao, Hai-Qiong; Yu, Guo-Fu

2017-04-01

In this paper, a spatial discrete complex modified Korteweg-de Vries equation is investigated. The Lax pair, conservation laws, Darboux transformations, and breather and rational wave solutions to the semi-discrete system are presented. The distinguished feature of the model is that the discrete rational solution can possess new W-shape rational periodic-solitary waves that were not reported before. In addition, the first-order rogue waves reach peak amplitudes which are at least three times of the background amplitude, whereas their continuous counterparts are exactly three times the constant background. Finally, the integrability of the discrete system, including Lax pair, conservation laws, Darboux transformations, and explicit solutions, yields the counterparts of the continuous system in the continuum limit.

Empirical solution of Green-Ampt equation using soil conservation service - curve number values

NASA Astrophysics Data System (ADS)

Grimaldi, S.; Petroselli, A.; Romano, N.

2012-09-01

The Soil Conservation Service - Curve Number (SCS-CN) method is a popular widely used rainfall-runoff model for quantifying the total stream-flow volume generated by storm rainfall, but its application is not appropriate for sub-daily resolutions. In order to overcome this drawback, the Green-Ampt (GA) infiltration equation is considered and an empirical solution is proposed and evaluated. The procedure, named CN4GA (Curve Number for Green-Ampt), aims to calibrate the Green-Ampt model parameters distributing in time the global information provided by the SCS-CN method. The proposed procedure is evaluated by analysing observed rainfall-runoff events; results show that CN4GA seems to provide better agreement with the observed hydrographs respect to the classic SCS-CN method.

Upwind methods for the Baer–Nunziato equations and higher-order reconstruction using artificial viscosity

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

Fraysse, F., E-mail: francois.fraysse@rs2n.eu; E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid; Redondo, C.

This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is appliedmore » to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.« less