Optimization Of TVB Limiter On Discontious Galerkin Method

The limiter is an important factor that affects the accuracy,stability and convergence of the calculation,also an key mean to improve the resolution of a scheme.Howerve,the dissipation of the limiter results in good or bad results.When the dissipation is large,it may degenerate the accuracy at smooth extrema of the solution and lead to that shock is not sharp and fine structure is difficult to observe.When the dissipation is small,the numerical result may occur non-physical oscillation near the shock.In this paper,the concept of adaptive limiter is proposed and applied to the minmod-type TVB limiter proposed by Shu et al.The original TVB limiter,for the system case,is difficult to choose parameter M,whose choice depends on the solution of problem.In order to solve this problem,the initial condition and the rate of change in total variation of time are considered to determine the value of M.It'll make M value piecewise and adaptively.Numerical results by high order discontinuous galerkin in one dimension and two dimension several typical examples illustrate that this improved method can capture sharp shock.Also,the number of cells which are limited is in a normal level.What's more,the improved limiter is sensitive to the fine structure of flow field.The woke in this paper lays foundation of developing new adaptive limiter.