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On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
On maximum-principle-satisfying high order schemes for scalar conservation laws
Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
- Xiangxiong Zhang, Chi-Wang Shu
- Computer ScienceProceedings of the Royal Society A: Mathematical…
- 8 October 2011
This paper presents a simpler implementation of genuinely high-order accurate finite volume and discontinuous Galerkin schemes satisfying a strict maximum principle for scalar conservation laws, which will result in a significant reduction of computational cost especially for weighted essentially non-oscillatory finite-volume schemes.
Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes
This paper introduces a special quadrature rule which is exact for two-variable polynomials over a triangle of a given degree and satisfies a few other conditions, by which it can construct high order maximum principle satisfying finite volume schemes.
Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations
Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms
On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations
- Xiangxiong Zhang
- MathematicsJ. Comput. Phys.
Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes
The simple positivity-preserving limiter is reformulated, and it is proved that the resulting scheme guarantees the positivity of the water depth, as well as well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.