seminar

In this talk, we introduce a high-order, conservative, and positivity-preserving interpolation scheme which is developed based on the DG solution of a linear time-dependent equation on deforming meshes with arbitrary deformation. The scheme is aimed to be used for indirect ALE and rezoning moving mesh methods. The cost and positivity preservation (with a linear scaling limiter) of the DG-interpolation are investigated. Numerical examples are presented to demonstrate the properties of the interpolation scheme. The DG-interpolation is applied to the rezoning moving mesh DG solution of the radiative transfer equation. Numerical results obtained for examples in one and two spatial dimensions with various settings show that the resulting rezoning moving mesh DG method maintains the same convergence order as the standard DG method, is more efficient than the method with a fixed uniform mesh, and is able to preserve the positivity of the radiative intensity.