Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
A high-order discontinuous Galerkin method for 2D incompressible flows
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations
Journal of Computational Physics
A discontinuous Galerkin method for the Vlasov-Poisson system
Journal of Computational Physics
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
Journal of Computational Physics
The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
High Order Finite Difference and Finite Volume Methods for Advection on the Sphere
Journal of Scientific Computing
A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer
Journal of Computational Physics
SIAM Journal on Scientific Computing
Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation
Journal of Computational Physics
Journal of Computational Physics
Positivity-preserving DG and central DG methods for ideal MHD equations
Journal of Computational Physics
Journal of Scientific Computing
Discontinuous Galerkin method for Krause's consensus models and pressureless Euler equations
Journal of Computational Physics
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
Journal of Computational Physics
Journal of Computational Physics
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.54 |
We construct uniformly high order accurate schemes satisfying a strict maximum principle for scalar conservation laws. A general framework (for arbitrary order of accuracy) is established to construct a limiter for finite volume schemes (e.g. essentially non-oscillatory (ENO) or weighted ENO (WENO) schemes) or discontinuous Galerkin (DG) method with first order Euler forward time discretization solving one-dimensional scalar conservation laws. Strong stability preserving (SSP) high order time discretizations will keep the maximum principle. It is straightforward to extend the method to two and higher dimensions on rectangular meshes. We also show that the same limiter can preserve the maximum principle for DG or finite volume schemes solving two-dimensional incompressible Euler equations in the vorticity stream-function formulation, or any passive convection equation with an incompressible velocity field. Numerical tests for both the WENO finite volume scheme and the DG method are reported.