We analyze the convergence for relaxation approximation applied to conservation laws with stiff source terms. We suppose that the source term q(u) is dissipative. Semi-implicit relaxing schemes are investigated and the corresponding stability theory is established. In particular, we proved that the numerical solution of a first-order relaxing scheme is uniformlly Z, I and TVstable, in the sense...

A procedure to switch the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be stable and accurate. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition shock calculations is performed, using a scheme where the develope...

A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing SummationBy-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the...

In this work a new coupled level set volume tracking method is introduced. To advance the solution in time, a MUSCL-type method combined to a new flux limiter is used. It is shown that our discrete method has many interesting properties that make it suitable for problems where the tracking of a large number of regions is needed. A dedicated reconstruction algorithm for the level set reinizializ...

Fully implicit, fully coupled techniques are developed for simulating multiphase flow with nonequilibrium mass transfer between phases, with application to groundwater contaminant flow and transport. Numerical issues which are addressed include: use of MUSCL or Van Leer flux limiters to reduce numerical dispersion, use of full or approximate Jacobian for flux limiter methods, and variable subst...

This article presents a numerical study of turbulent flow around a generic three-dimensional prolate spheroid with a 20◦ angle of attack. The Reynolds number we use is a moderate one Re = 4 × 104. In this work we compare three different turbulence models : the RANS k − ε, the LES Smagorinsky and the VMS-LES. The numerical code makes use of a mixed FE/FV formulation based on tetrahedra. A Roe’s ...