A high order positivity-preserving conservative WENO remapping method on 3D tetrahedral meshes

Abstract

We propose a high order positivity-preserving conservative remapping method on three-dimensional (3D) tetrahedral meshes, based on the weighted essentially non-oscillatory (WENO) reconstruction method. By precisely computing the overlaps between the meshes before and after the rezoning step in the arbitrary Lagrangian–Eulerian (ALE) framework, our method does not limit the range of mesh movements and has wider applications. This also makes our remapping process simpler to attain high-order accuracy. We use the third order multi-resolution WENO reconstruction procedure in this paper as an example, in which we reconstruct three polynomials of different orders via nested central spatial stencils and distribute nonlinear weights based on the smoothness of the polynomials, ensuring optimal accuracy in the smooth region while avoiding numerical oscillations in the non-smooth region. The multi-resolution WENO procedure involves fewer high-order reconstruction polynomials and can use arbitrary positive linear weights, making it more effective for our 3D remapping problem. We incorporate an efficient local limiting to preserve positivity for the positive physical variables involved in the ALE framework without sacrificing the original high-order accuracy and conservation. A set of numerical tests are provided to verify properties of our remapping algorithm, such as high-order accuracy, conservation, essentially non-oscillatory performance, positivity-preserving and efficiency.