A REVIEW ON HIGH ORDER WELL-BALANCED PATH-CONSERVATIVE FINITE VOLUME SCHEMES FOR GEOPHYSICAL FLOWS

摘要

In this work a general strategy to design high order well-balanced schemes for hyperbolic system with nonconservative products and/or source terms is reviewed. We briefly recall the theory of Dal Maso-LeFloch-Murat to define weak solutions of nonconservative systems and how it has been used to establish the notion of path-conservative schemes. Next, a family of high order finite volume methods combining a reconstruction operator and a first order path-conservative scheme is described. Then, the well-balanced property of the proposed methods is analyzed. Finally, some challenging examples on tsunami modeling are shown.