Solitary Wave Benchmarks in Magma Dynamics

TL;DR

This paper introduces a benchmark problem based on solitary wave solutions in magma dynamics, enabling evaluation of numerical methods for modeling magma migration within Earth's interior.

Contribution

It presents a new benchmark problem with exact solitary wave solutions for magma dynamics and demonstrates a novel algorithm for approximating these waves to test numerical schemes.

Findings

Successful computation of high-quality solitary wave approximations

Benchmarking of a semi-Lagrangian Crank-Nicholson scheme

Validation of the new algorithm's effectiveness

Abstract

We present a model problem for benchmarking codes that investigate magma migration in the Earth's interior. This system retains the essential features of more sophisticated models, yet has the advantage of possessing solitary wave solutions. The existence of such exact solutions to the nonlinear problem make it an excellent benchmark problem for combinations of solver algorithms. In this work, we explore a novel algorithm for computing high quality approximations of the solitary waves and use them to benchmark a semi-Lagrangian Crank-Nicholson scheme for a finite element discretization of the time dependent problem.