Moments Preserving and high-resolution Semi-Lagrangian Advection Scheme

TL;DR

This paper introduces a high-order, moments-preserving semi-Lagrangian advection scheme capable of accurately handling smooth and discontinuous fields, with efficient parallel implementation for multi-dimensional simulations.

Contribution

The paper presents a novel semi-Lagrangian method combining non-linear mapping and adaptive interpolation for high-accuracy advection of complex fields.

Findings

High-order accuracy in advecting smooth and discontinuous fields

Effective parallelization on many-core architectures

Validated through multi-dimensional advection tests

Abstract

We present a forward semi-Lagrangian numerical method for systems of transport equations able to advect smooth and discontinuous fields with high-order accuracy. The numerical scheme is composed of an integration of the transport equations along the trajectory of material elements in a moving grid and a reconstruction of the fields in a reference regular mesh using a non-linear mapping and adaptive moment-preserving interpolations. The non-linear mapping allows for the arbitrary deformation of material elements. Additionally, interpolations can represent discontinuous fields using adaptive-order interpolation near jumps detected with a slope-limiter function. Due to the large number of operations during the interpolations, a serial implementation of this scheme is computationally expensive. The scheme has been accelerated in many-core parallel architectures using a thread per grid node and parallel data gathers. We present a series of tests that prove the scheme to be an attractive option for simulating advection equations in multi-dimensions with high accuracy.