Solution Limiters and Flux Limiters for High Order Discontinuous Galerkin Schemes
نویسنده
چکیده
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 that β should be 0 < β < 1 for a monotone approximate solution.
منابع مشابه
The multi-dimensional limiters for discontinuous Galerkin method on unstructured grids
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...
متن کاملOn positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations
We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to high dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta tim...
متن کاملA DGBGK scheme based on WENO limiters for viscous and inviscid flows
This paper presents a discontinuous Galerkin BGK (DGBGK) method for both viscous and inviscid flow simulations under a DG framework with a gas-kinetic flux and WENO limiters. In the DGBGK method, the construction of the flux in the DG method is based on the particle transport and collisional mechanism which not only couples the convective and dissipative terms together, but also includes both d...
متن کاملThe multi-dimensional limiters for discontinuous Galerkin methods on unstructured grids
High order limiters remain one of the main challenges for discontinuous Galerkin (DG) methods in solving hyperbolic conservation laws. This paper proposes an efficient limiting procedure for the DG method. The key feature is to construct additional polynomials from the solutions on neighboring cells by means of secondary reconstruction. Then the limited solution on current cell can be obtained ...
متن کاملDevelopment and Comparison of Numerical Fluxes for LWDG Methods
The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The LaxWendroff time discretization procedure is an alternative method for time d...
متن کامل