Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations

TL;DR

This paper develops and evaluates second-order accurate ADER-type schemes for advection-diffusion-reaction equations, focusing on stability, accuracy, and practical implementation for industrial applications.

Contribution

It introduces and analyzes new ADER and MUSCL-Hancock based schemes with detailed stability and error analysis, validated through empirical convergence tests.

Findings

Schemes achieve expected second-order accuracy in space and time.

Stability analysis confirms linear stability under certain conditions.

Empirical tests validate theoretical convergence rates.

Abstract

We construct, analyse and assess various schemes of second order of accuracy in space and time for model advection-diffusion-reaction differential equations. The constructed schemes are meant to be of practical use in solving industrial problems and are derived following two related approaches, namely ADER and MUSCL-Hancock. Detailed analysis of linear stability and local truncation error are carried out. In addition, the schemes are implemented and assessed for various test problems. Empirical convergence rate studies confirm the theoretically expected accuracy in both space and time.