Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations

By Richard Liska, Burton Wendroff. SIAM Journal on Scientific Computing, 2003

398 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/08dc2ab24ae95aa5d2d7e1ec9c29531ae675a8c8

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Eulerian-Lagrangian modelling of detonative combustion in two-phase gas-droplet mixtures with OpenFOAM: Validations and verifications (2020, methodology): “The multicomponent (H2/O2/Ar) reactive shock tube is first investigated by Oran et al. [50], and has been widely used to evaluate the performance of numerical methods and implementations for compressible reactive flows, e.g. in Refs.”
An unsplit Godunov method for ideal MHD via constrained transport (2005, methodology): “The solution to the one dimensional Riemann problem has long been used as a test of numerical algorithms [30,21].”
Entropy viscosity method for nonlinear conservation laws (2011, methodology): “The Fourier result compares well with those from [23].”
A high-order finite volume method for systems of conservation laws - Multi-dimensional Optimal Order Detection (MOOD) (2011, methodology): “Then we proceed with a 2D Riemann problem proposed by [25] (see also [18]).”
The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers (2020, background): “Liska–Wendroff Implosion The implosion test discussed in §4.7 of Liska & Wendroff (2003) and first introduced in Hui et al. (1999) is an extraordinarily sensitive test of the directional symmetry-preserving abilities of a hydrodynamics code.”
Athena: A New Code for Astrophysical MHD (2008, result): “Many of the problems are drawn from test suites of our own codes (Stone et al. 1992a) or from those published by other authors (Woodward & Colella 1984, hereafter WC84; Ryu & Jones1995, hereafter RJ95; T2000; Liska & Wendroff 2003, hereafter LW03).”
Smoothed Particle Hydrodynamics in Astrophysics (2010, background): “We now a discuss a yet more demanding two-dimensional problem, the vortex test of Gresho (Gresho & Chan, 1990; Liska & Wendroff, 2003).”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, methodology): “The methods fail on all the cosmological tests and strongly self-gravitating tests, as well as the Noh problem (see Liska & Wendroff 2003) and the interacting blastwave of which can be summarized within the context of the “reproducing kernel particle method” as generally developed in Liu et al.…”
Improving convergence in smoothed particle hydrodynamics simulations without pairing instability (2012, background): “A critical test of this situation consists of a differentially rotating fluid of uniform density in centrifugal balance (Gresho & Chan 1990, see also Liska & Wendroff 2003; Springel 2010; Read & Hayfield 2012).”
Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves (2010, methodology): “, shock-capturing schemes for shock-dominated flows [29,16]; artificial diffusivity methods for shocks [7,13,22] or purely broadband problems [8,6]; and monotone integrated LES or MILES [17], subgrid-scale modeling for LES [24] and the evaluation of shock-capturing schemes in LES [15] for compressib”
An improved reconstruction method for compressible flows with low Mach number features (2008, background): “Both original and modified schemes demonstrate excellent shock capturing, however both schemes break symmetry (as do many high order schemes in this test case (see Liska and Wendroff [12]), and are oscillatory behind the strong shock.”
On the Reduction of Numerical Dissipation in Central-Upwind Schemes (2007, methodology): “Example 5: Explosion In the final example, we compute the so-called explosion problem proposed in [30] (see also [27], where different numerical schemes were tested on this problem).”