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Entropy stable schemes for initial-boundary-value conservation laws
(2010)SAM Research ReportWe consider initial boundary value problems for systems of conservation laws and design entropy stable finite difference schemes to approximate them. The schemes are shown to be entropy stable for a large class of systems that are equipped with a symmetric splitting, derived from the entropy formulation. Numerical examples for the Euler equations of gas dynamics are presented to illustrate the robust performance of the proposed method.Report -
Sparse Tensor Multi-Level Monte Carlo Finite Volume Methods for hyperbolic conservation laws with random intitial data
(2010)SAM Research ReportWe consider scalar hyperbolic conservation laws in several $(d \ge 1)$ spatial dimensions with stochastic initial data. We prove existence and uniqueness of a random-entropy solution and show existence of statistical moments of any order k of this random entropy solution. We present a class of numerical schemes of multi-level Monte Carlo Finite Volume (MLMC-FVM) type for the approximation of random entropy solutions as well as of their ...Report