Numerical Analysis and Scientific Computing | Mathematics in Science and Technology
Invited Lecture 15.1 | 17.1
A review on high order well-balanced path-conservative finite volume schemes for geophysical flows
Manuel Castro

Abstract: 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.

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