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

Liska, R.; Wendroff, Burton

doi:10.1137/s1064827502402120

Cited by 340 publications

(346 citation statements)

References 50 publications

Supporting

Mentioning

304

Contrasting

Unclassified

Order By: Relevance

“…The 2D simulation ends at t = 2.0. According to Liska and Wendroff [17], many high-resolution schemes produce highly oscillatory results or simply crash in this test. Using the synchronized (ρ, E, p) limiter and the new sequential (ρ, E, k) limiter to constrain the DG-HLL-P 1 approximation, we obtained the results presented in Fig.…”

Section: Noh Problemmentioning

confidence: 99%

See 1 more Smart Citation

Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

Dobrev

Kolev

Kuzmin

et al. 2018

Journal of Computational Physics

View full text Add to dashboard Cite

We present a new approach to enforcing local maximum principles in finite element schemes for the compressible Euler equations. In contrast to synchronized limiting techniques for systems of conservation laws, the density, momentum, and total energy are constrained in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum are adjusted to incorporate the irreversible effect of density changes. Then the corresponding antidiffusive corrections are limited to satisfy inequality constraints for the total and kinetic energy. The same element-based limiting strategy is employed in the context of continuous and discontinuous Galerkin methods. The sequential nature of the new limiting procedure makes it possible to achieve crisp resolution of contact discontinuities while using sharp local bounds in the energy constraints. A numerical study is performed for piecewise-linear finite element discretizations of 1D and 2D test problems.

show abstract

Section: Noh Problemmentioning

confidence: 99%

“…In contrast to the previous examples, the adiabatic constant is γ = 5/3. The exact solution is the infinite strength symmetric shock [17] ρ(x, y, t) = 1 + t/ x 2 + y 2 if x 2 + y 2 > t/3, 16 otherwise,…”

Section: Noh Problemmentioning

confidence: 99%

Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

Dobrev

Kolev

Kuzmin

et al. 2018

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…Для этой задачи не существует точного решения. В качестве эталонного принимается решение [12], полученное при помощи метода кусочно-параболической реконструкции на сетке, содержащей 2000 ячеек. В работе [19] задача используется в качестве теста для алгоритмов решения уравнений Эйлера на сетках, динамически адап-тирующихся к решению.…”

Section: обзор задачunclassified

“…В работе [12] приводятся решения 10 одномерных задач газовой динамики при помощи различных разностных схем (всего рассматривается 8 разностных схем). Представленные результаты достаточно полно представляют возможности конечно-объемных методов к решению уравнений Эйлера.…”

Section: Introductionunclassified

See 1 more Smart Citation

WENO schemes for solution of unsteady one-dimensional gas dynamics test problems

Bulat¹,

Volkov²

2016

Naučno-teh. vestn. inf. tehnol. meh. opt.

View full text Add to dashboard Cite

A comparative study of TVD‐limiters—well‐known limiters and an introduction of new ones

Kemm

2011

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYThis paper gives a comparative study of TVD-limiters for standard explicit Finite Volume schemes. In contrast to older studies, it includes also unsymmetrical limiter functions that depend on the local CFLnumber. We classify the limiters and show how to extend these families of limiters. We introduce a new member of the Superbee family, which is adapted to Roe's linear third-order scheme. Based on an idea by Serna and Marquina, new smooth limiters are introduced, which turn the van Leer and van Albada limiters into complete classes of limiters. The comparison of the limiters is done with some standard test cases. The results clarify the influence of the chosen limiter on the quality of the numerical results. Compared with ENO or WENO schemes, they also show the high resolution, which can be obtained by a CFL-number-dependent limiter when the grid is not highly refined.

show abstract

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

Cited by 340 publications

References 50 publications

Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

WENO schemes for solution of unsteady one-dimensional gas dynamics test problems

A comparative study of TVD‐limiters—well‐known limiters and an introduction of new ones

Contact Info

Product

Resources

About