We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not restricted to certain classes of hydrostatic solutions. In one spatial dimension we construct a method that exactly balances a high order discretization of any hydrostatic state. The method is extended to two spatial dimensions using a local high order approximation of a hydrostatic state in each cell. The proposed simple, flexible, and robust methods are not restricted to a specific equation of state. Numerical tests verify that the proposed method improves the capability to accurately resolve small perturbations on hydrostatic states.
Low-Shapiro hydrostatic reconstruction technique for blood flow simulation in large arteries with varying geometrical and mechanical properties
Laboratoire J.A. Dieudonné, UMR CNRS 7351 & Polytech’ Nice Sophia, University of Nice Sophia Antipolis (UNS)（J.A. 迪厄多内实验室，UMR CNRS 7351 和尼斯索菲亚安蒂波利斯理工学院，尼斯索菲亚安蒂波利斯大学）
Second order finite volume scheme for Euler equations with gravity which is well-balanced for general equations of state and grid systems
Univ. of Würzburg（维尔茨堡大学）；TIFR Center for Applicable Mathematics（TIFR应用数学中心）；Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik（海德堡大学天文学中心，理论天体物理研究所）；Heidelberger Institut für Theoretische Studien（海德堡理论研究所）
