In this paper, we present a class of parametrized limiters used to achieve strict maximum principle for high order numerical schemes applied to hyperbolic conservation laws computation. By decoupling a sequence of parameters embedded in a group of explicit inequalities, the numerical fluxes are locally redefined in consistent and conservative formulation. We will show that the global maximum pr...

The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is explored and bounds derived for such limiters. A class of limiters is presented which includes a very compressive limiter due to Roe, and various limiters are compared both theoretically and numerically.

We analyze a general concept of limiters for a high order DG scheme written for a 1-D problem. The limiters, which are local and do not require extended stencils, are incorporated into the solution reconstruction in order to meet the requirement of monotonicity and avoid spurious solution overshoots. A limiter β will be defined based on the solution jumps at grid interfaces. It will be shown th...

2-d and axisymmetric navier-stokes equations are solved using reiman-roe solver with different limiters for second-order accurate schemes. the results were obtained for supersonic viscous flows over semi-infinite axisymmetric and 2-d bodies. the free stream mach numbers were 7.78 and 16.34. the stability of roe method with different limiters and entropy conditions were considered. the results s...

In Xu [11], a class of parametrized flux limiters is developed for high order finite difference/volume essentially non-oscillatory (ENO) and Weighted ENO (WENO) schemes coupled with total variation diminishing (TVD) Runge-Kutta (RK) temporal integration for solving scalar hyperbolic conservation laws to achieve strict maximum principle preserving (MPP). In this paper, we continue along this lin...

2-D and axisymmetric Navier-Stokes equations are solved using Reiman-Roe solver with different limiters for second-order accurate schemes. The results were obtained for supersonic viscous flows over semi-infinite axisymmetric and 2-D bodies. The free stream Mach numbers were 7.78 and 16.34. The stability of Roe method with different limiters and entropy conditions were considered. The results s...

2-D and axisymmetric Navier-Stokes equations are solved using Reiman-Roe solver with different limiters for second-order accurate schemes. The results were obtained for supersonic viscous flows over semi-infinite axisymmetric and 2-D bodies. The free stream Mach numbers were 7.78 and 16.34. The stability of Roe method with different limiters and entropy conditions were considered. The results s...

In Xu [14], a class of parametrized flux limiters is developed for high order finite difference/volume essentially non-oscillatory (ENO) and Weighted ENO (WENO) schemes coupled with total variation diminishing (TVD) Runge-Kutta (RK) temporal integration for solving scalar hyperbolic conservation laws to achieve strict maximum principle preserving (MPP). In this paper, we continue along this lin...

Accuracy-preserving and non-oscillatory shock-capturing technique is the bottle neck in the development of discontinuous Galerkin method. Inspired by the success of the k-exact WENO limiters for high order finite volume methods, this paper generalize the k-exact WENO limiter to discontinuous Galerkin methods. Also several improvements are put forward to keep the compactness and high-order accur...

Limiters are nonlinear hybridization techniques that are used to preserve positivity and monotonicity when numerically solving hyperbolic conservation laws. Unfortunately, the original methods suffer from the truncation-error being 1 order accurate at all extrema despite the accuracy of the higher-order method [1, 2, 3, 4]. To remedy this problem, higherorder extensions were proposed that relie...