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 ...

In [20], Qiu and Shu investigated using weighted essentially non-oscillatory (WENO) finite volume methodology as limiters for the Runge-Kutta discontinuous Galerkin (RKDG) methods for solving nonlinear hyperbolic conservation law systems on structured meshes. In this continuation paper, we extend the method to solve two dimensional problems on unstructured meshes, with the goal of obtaining a r...

Abstract In this paper, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) limiters, for the RungeKutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation laws. This new HWENO limiter is a modification of the simple WENO limiter proposed recently by Zhong and Shu [32]. Both limiters use information ...

Novel limiters based on the weighted average procedure are developed for finite volume methods solving multi-dimensional hyperbolic conservation laws on unstructured grids. The development of these limiters is inspired by the biased averaging procedure of Choi and Liu [10]. The remarkable features of the present limiters are the new biased functions and the weighted average procedure, which ena...

In recent years finite volume computations of two-fluid hydrodynamic models have been used in a number of numerical investigations of gas-solids fluidized bed and circulating fluidized bed processes. To avoid numerical diffusion from dominating simulation results, proper discretization of convective terms is critical i e higher-order methods should be used in the computation of convective terms...

Parallel heat flux in a steady-state SOL is determined via fully kinetic simulations using the 1d3v particle-in-cell code PARASOL. In order to better evaluate the heat load on the divertor plates, the ion and electron velocity distributions functions (VDF), heat flux, and heat flux limiters αi and αe are calculated. The effects of collisionality, recycling rate, ion-electron mass ratio, and sou...

New Car Assessment Program (NCAP) test scores, measured by the United States Department of Transportation's (USDOT) National Highway Traffic Safety Administration (NHTSA), were analyzed in order to assess the benefits of equipping safety belt systems with pretensioners and load limiters. Safety belt pretensioners retract the safety belt almost instantly in a crash to remove excess slack. They t...

The maximum principle is an important property of solutions to PDE. Correspondingly, it’s of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO s...