Semi-Implicit-type order-adaptive CAT2 schemes for systems of balance laws with relaxed source term
Abstract
In this paper we present two semi-implicit-type second order Compact Approximate Taylor (CAT2) numerical schemes and blend them with a local a posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve hyperbolic systems of balance laws with relaxed source term. The resulting scheme presents high accuracy when applied to smooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearly fail-safe property in terms of ensuring positivity. The numerical results obtained from a variety of test cases, including smooth and non-smooth well-prepared and unprepared initial condition, assessing the appropriate behavior of the semi-implicit-type second order CATMOOD schemes. These results have been compared in accuracy and efficiency with a second order semi-implicit Runge-Kutta (RK) method.
Keywords
Cite
@article{arxiv.2309.13954,
title = {Semi-Implicit-type order-adaptive CAT2 schemes for systems of balance laws with relaxed source term},
author = {E. Macca and S. Boscarino},
journal= {arXiv preprint arXiv:2309.13954},
year = {2023}
}