High order entropy stable and positivity-preserving discontinuous Galerkin method for the nonlocal electron heat transport model

Abstract

The nonlocal electron heat transport model in laser heated plasmas plays a crucial role in inertial confinement fusion (ICF), and it is important to solve it numerically in an accurate and robust way. In this paper, we first develop an one-dimensional high-order entropy stable discontinuous Galerkin method for the nonlocal electron heat transport model. We further design our DG scheme to have the positivity-preserving property by using the scaling positivity-preserving limiter, which is shown, by a computer-aided proof, to have no extra time step constraint than that required by L2 stability. Next, we extend our one-dimensional scheme to two-dimensions on rectangular meshes and tensor product polynomial spaces. Numerical examples are given to verify the high-order accuracy and positivity-preserving properties of our scheme. By comparing the local and nonlocal electron heat transport models, we also observe more physical phenomena such as the flux reduction and the preheat effect from the nonlocal model.