Invited Lecture
Implicit and semi-implicit high-order well-balanced methods for systems of balance laws
Universidad de Málaga, Spain
Abstract
The goal of this work is to design implicit and semi-implicit high-order well-balanced numerical methods for systems of balance laws with stiff numerical flux and source term. Here we use the general strategy introduced by Castro-Pares (2020) to construct high-order well-balanced reconstruction operators that are combined with standard RK-IMEX or RK-Implicit to integrate in time the balance laws. We will show that strategy that we propose is able to maintain the properties of the RK-IMEX and RK-implicit method design for the homogenous system and the well-balanced property of the reconstruction operator, ensuring the well-balanced character of the resulting methods. This general strategy will be applied to several systems of balance laws, such as the Burgers equation with source term or the 1D shallow water system.