Manuel Torrilhon

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A new closure for Grad’s 13 moment equations is presented that adds terms of SuperBurnett order to the balances of pressure deviator and heat flux vector. The additional terms are derived from equations for higher moments by means of the distribution function for 13 moments. The resulting system of equations contains the Burnett and Super-Burnett equations(More)
This paper presents the technical details necessary to implement an exact solver for the Riemann problem of magnetohydrodynamics (MHD) and investigates the uniqueness of MHD Riemann solutions. The formulation of the solver results in a nonlinear algebraic 5 × 5 system of equations which has to be solved numerically. The equations of MHD form a non-strict(More)
This paper presents Riemann test problems for ideal MHD finite volume schemes. The test problems place emphasis on the hyperbolic irregularities of the ideal MHD system, namely the occurrence of intermediate shocks and non-unique solutions. We investigate numerical solutions for the test problems obtained by several commonly used methods (Roe, HLLE, central(More)
A general framework for constructing constraint-preserving numerical methods is presented and applied to a multidimensional divergence-constrained advection equation. This equation is part of a set of hyperbolic equations that evolve a vector field while locally preserving either its divergence or curl. We discuss the properties of these equations and their(More)
Boundary conditions are the major obstacle in simulations based on advanced continuum models of rarefied and micro-flows of gases. In this paper we present a theory how to combine the regularized 13-moment-equations derived from Boltzmann’s equation with boundary conditions obtained from Maxwell’s kinetic accommodation model. While for the linear case these(More)
It is of utmost interest to control the divergence of the magnetic flux in simulations of the ideal magnetohydrodynamic equations since, in general, divergence errors tend to accumulate and render the schemes unstable. This paper presents a higher-order extension of the locally divergence-preserving procedure developed in Torrilhon [M. Torrilhon, Locally(More)
In this thesis we consider finite volume methods for the numerical solution of conservation laws modeled by systems of nonlinear hyperbolic partial differential equations. We are in particular interested in highorder accurate numerical approximations of conservation laws. Numerical approximations of nonlinear hyperbolic partial differential equation are(More)