SEARCH · Search NASA

Results for “Riemann solvers”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

All sources NASA NTRS DOE OSTI

NASA NTRS1991

An adaptively-refined Cartesian mesh solver for the Euler equations

A method for adaptive refinement of a Cartesian mesh for the solution of the steady Euler equations is presented. The algorithm creates an initial uniform mesh and cuts the body out of that mesh. The mesh is then refined based on body curvature. Next, the solution is converged to a steady state using a linear reconstruction and Roe's approximate Riemann solver. Solution-adaptive refinement of the mesh is then applied to resolve high-gradient regions of the flow. The numerical results presented show the flexibility of this approach and the accuracy attainable by solution-based refinement.

De Zeeuw, Darren↗

DOE OSTI2020

Finite Volume Discretization of the Euler Equations in Pronghorn

Modeling flow and heat transfer in high temperature gas reactors (HTGR) requires the ability to model a wide range of flow speeds from slow (natural convection), to intermediate (forced-flow conditions), to supersonic regimes (depressurization) for a wide range of geometries including the pebble bed, upper and lower plenum, and risers. In previous work, Pronghorn has effectively modeled low-to-medium speed flows in scenarios such as the one described in the two-dimensional PBMR-400 benchmark, using its finite-element-based streamline-upwind Petrov-Galerkin (SUPG) stabilized implementation of the Euler equations. However, limitations of this method become apparent when dealing with more complicated geometries (e.g. imposing slip boundary conditions at nodes belonging to two different boundaries) and when gas speeds are fast enough for shocks and supersonic flow to occur. For these problems, the finite-element-based solver lacks robustness and is plagued by slow iterative convergence or even divergence. In order to address these challenges, the Pronghorn code at INL has been updated with new, modified versions of its original equations. The new Pronghorn models are built on the finite volume method with a Harten-Lax-van Leer-Contact (HLLC) Riemann solver based numerical flux method, which (1) allows imposing slip boundary conditions much more robustly and (2) performs well for a wide range of flow speeds. The finite-volume-based flow solver will form the basis for a robust coarse-mesh thermal-hydraulics capability in Pronghorn.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1995

New higher-order Godunov code for modelling performance of two-stage light gas guns

A new quasi-one-dimensional Godunov code for modeling two-stage light gas guns is described. The code is third-order accurate in space and second-order accurate in time. A very accurate Riemann solver is used. Friction and heat transfer to the tube wall for gases and dense media are modeled and a simple nonequilibrium turbulence model is used for gas flows. The code also models gunpowder burn in the first-stage breech. Realistic equations of state (EOS) are used for all media. The code was validated against exact solutions of Riemann's shock-tube problem, impact of dense media slabs at velocities up to 20 km/sec, flow through a supersonic convergent-divergent nozzle and burning of gunpowder in a closed bomb. Excellent validation results were obtained. The code was then used to predict the performance of two light gas guns (1.5 in. and 0.28 in.) in service at the Ames Research Center. The code predictions were compared with measured pressure histories in the powder chamber and pump tube and with measured piston and projectile velocities. Very good agreement between computational fluid dynamics (CFD) predictions and measurements was obtained. Actual powder-burn rates in the gun were found to be considerably higher (60-90 percent) than predicted by the manufacturer and the behavior of the piston upon yielding appears to differ greatly from that suggested by low-strain rate tests.

Bogdanoff, D. W.↗

NASA NTRS1993

A new Lagrangian method for three-dimensional steady supersonic flows

In this report, the new Lagrangian method introduced by Loh and Hui is extended for three-dimensional, steady supersonic flow computation. The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) scheme is presented. This new approach is accurate and robust, capable of handling complicated geometry and interactions between discontinuous waves. Test problems show that the extended Lagrangian method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation). In this report, we also suggest a novel three dimensional Riemann problem in which interesting and intricate flow features are present.

Loh, Ching-Yuen↗

DOE OSTI2022

Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

Here, a high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation, and an exact Riemann solver is employed to compute the numerical flux at the interface between dissimilar materials with general anisotropic properties. The space-discretized equations are then advanced in time using explicit high-order Runge–Kutta algorithms. Several two- and three-dimensional numerical tests including dynamic adaptive mesh refinement are presented to demonstrate the high-order accuracy and the capability of the method in the elastodynamic analysis of single- and bi-phases solids containing complex geometries.

42 ENGINEERING↗

DOE OSTI2020

A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation

In this work, a high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for solving two-dimensional hydrodynamic problems in cell-centered updated Lagrangian formulation. This method is the Lagrangian limit of the unsplit rDG-ALE formulation, and is obtained by assuming the equality of the grid velocity to the fluid velocity only at cell boundaries. The conservative variables and the Taylor basis defined on the time-dependent moving mesh, provide the piece-wise polynomial expansion in the updated Lagrangian formulation. A multi-directional nodal Riemann solver is implemented for computing the grid velocity at the vertices and the numerical flux at the cell boundaries. A characteristic limiting procedure is extended from the primitive variable version to the conservative variable version, and its performance is compared with the limiter on physical variables. A number of benchmark test cases are conducted to assess the accuracy, robustness, and non-oscillatory property of the DG(P0), DG(P1) and rDG(P1P2) methods. The numerical experiments demonstrate that the developed rDG method is able to attain the designed order of accuracy and the characteristic limiting procedure outperforms the limiter on physical variables in terms of the monotonicity and symmetry preservation for shock problems.

42 ENGINEERING↗

DOE OSTI2020

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

FSISPH: An SPH formulation for impacts between dissimilar materials

Here, we present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics

Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. In conclusion, we present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Asymptotic-preserving semi-implicit finite volume scheme for extended magnetohydrodynamics

A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such that it allows the algorithm to retain the use of ideal MHD Riemann solvers and the constrained transport method to preserve divergence-free magnetic fields. Incorporation of electron inertia and displacement current introduces additional numerical stiffness which motivates a semi-implicit FV scheme that re-formulates the XMHD model as a relaxation system. The equations are then advanced in time using an explicit 2nd-order Runge–Kutta scheme with operator splitting applied to the implicit source term updates at each sub-stage. For additional numerical stability, a density-dependent slope limiter is implemented to increase flux diffusivity at low density regions where non-ideal effects become significant. The algorithm is subsequently implemented in a scalable adaptive mesh refinement (AMR) framework. As the new algorithm retains many aspects of the ideal MHD formulations, it asymptotes naturally to the ideal MHD limit. Moreover, it shows promising results at the resistive and Hall MHD limits. This is verified against reference test problems for ideal, resistive and Hall MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Advection algorithms for quantum neutrino moment transport

Neutrino transport in compact objects is an inherently challenging multidimensional problem. Here, this difficulty is compounded if one includes flavor transformation—an intrinsically quantum phenomenon requiring one to follow the coherence between flavors and thus necessitating the introduction of complex numbers. To reduce the computational burden, simulations of compact objects that include neutrino transport often make use of momentum-angle-integrated moments (the lowest order ones being commonly referred to as the energy density and flux) and these quantities can be generalized to include neutrino flavor, i.e., they become quantum moments. Numerous finite-volume approaches to solving the moment evolution equations for classical neutrino transport have been developed based on solving a Riemann problem at cell interfaces. In this paper we describe our generalization of a Riemann solver for quantum moments, specifically decomposing complex numbers in terms of a (signed) magnitude and phase instead of real and imaginary parts. We then test our new algorithm in numerous cases showing a neutrino fast flavor instability, varying from toy models with analytic solutions to snapshots from neutron star merger simulations. Compared to previous algorithms for neutrino transport with flavor mixing, we find uniformly smaller growth rates of the flavor transformation along with concomitantly larger length-scales, and that the results are a better match with the growth rates seen from multiangle codes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Simulating Magnetic Reconnection in ‘Two Ribbon’ Type Solar Flares

Magnetic reconnection is an astrophysical process where neighboring magnetic field lines, facing anti-parallel, are reconfigured. This reconfiguration results in built up magnetic energy being explosively released as it is being converted to plasma kinetic and thermal energies. There are various kinds of simulations used to simulation reconnection; our work begins with Athena++, a magnetohydrodynamic (MHD) simulation code typically used for astrophysical problems, and a reconnection specific code file. The resistive MHD equations are solved with Riemann solvers. There was an initial test run without modifying the code to understand the dynamics of the simulation. We expand on the original reconnection problem file by implementing a radiative cooling term specific to the corona. The radiative cooling is theorized to have an effect on solar coronal plasma and magnetic reconnection dynamics. The cooling term will be tested with various parameters and compared to the case without cooling to study these dynamics. The condensation found in only the with cooling case emphasizes the importance of implementing this feature and will be later tested with a thermal conduction term. We want to determine the parameter regime where non-equilibrium cooling will be important for the reconnection dynamics.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1974

Rapid finite-difference computation of subsonic and transonic aerodynamic flows

Rapid iterative (or semidirect) computation methods are developed for the finite-difference solution of the nonlinear equations of subsonic and transonic aerodynamics. At each iteration, a fast, direct elliptic algorithm solves the entire computation field. In an application to subsonic flow over a lifting airfoil, the full nonlinear stream-function equation is solved. Finally, a direct Cauchy-Riemann solver is used for the nonlinear transonic small-disturbance equations for a biconvex airfoil. At M = 0.7, t/c = 0.1 (subcritical), three iterations on a 39 x 32 mesh (totaling 2.45 sec on an IBM 360/67 computer) obtain convergence within 0.1%. A slightly supercritical case requires seven iterations (6.75 sec) for convergence within 1%.

Martin, E. D.↗

NASA NTRS1983

Computational methods for ideal compressible flow

Conservative dissipative difference schemes for computing one dimensional flow are introduced, and the recognition and representation of flow discontinuities are discussed. Multidimensional methods are outlined. Second order finite volume schemes are introduced. Conversion of difference schemes for a single linear convection equation into schemes for the hyperbolic system of the nonlinear conservation laws of ideal compressible flow is explained. Approximate Riemann solvers are presented. Monotone initial value interpolation; and limiters, switches, and artificial dissipation are considered.

Vanleer, B.↗

NASA NTRS1986

A new approach for solving the three-dimensional steady Euler equations. I - General theory

The present iterative procedure combines the Clebsch potentials and the Munk-Prim (1947) substitution principle with an extension of a semidirect Cauchy-Riemann solver to three dimensions, in order to solve steady, inviscid three-dimensional rotational flow problems in either subsonic or incompressible flow regimes. This solution procedure can be used, upon discretization, to obtain inviscid subsonic flow solutions in a 180-deg turning channel. In addition to accurately predicting the behavior of weak secondary flows, the algorithm can generate solutions for strong secondary flows and will yield acceptable flow solutions after only 10-20 outer loop iterations.

Chang, S.-C.↗

NASA NTRS1987

A generalized procedure for constructing an upwind based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some linear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to scalar nonlinear equations and a constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance in numerical experiments. The formulation is extended to the nonlinear system. It is demonstrated that the present procedure can easily convert existing central or upwind, and second- or higher-order differencing schemes to preserve monotonicity and yield physically admissible solutions. The formulation is simple mathematically as well as numerically; both matrix-vector multiplication and Riemann solver are avoided. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made.

Liou, Meng-Sing↗

NASA NTRS1987

A generalized procedure for constructing an upwind-based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.

Liou, Meng-Sing↗

NASA NTRS1988

Hypersonic blunt body computations including real gas effects

The recently developed second-order explicit and implicit total variation diminishing (TVD) shock-capturing methods of the Harten and Yee, Yee, and van Leer types in conjunction with a generalized Roe's approximate Riemann solver of Vinokur and the generalized flux-vector splittings of Vinokur and Montagne for two-dimensional hypersonic real gas flows are studied. A previous study on one-dimensional unsteady problems indicated that these schemes produce good shock-capturing capability and that the state equation does not have a large effect on the general behavior of these methods for a wide range of flow conditions for equilibrium air. The objective of this paper is to investigate the applicability and shock resolution of these schemes for two-dimensional steady-state hypersonic blunt body flows. The main contribution of this paper is to identify some of the elements and parameters which can affect the convergence rate for high Mach numbers or real gases but have negligible effect for low Mach number cases for steady-state inviscid blunt body flows.

Montagne, J.-L.↗