Mechanisms underlying detonation initiation in 1-D and 2-D configurations are explored computationally. The strong state-sensitivity of the underlying chemical kinetics causes the reaction zones to be exceedingly thin, and accuracy of solution demands that the computational scheme provide the necessary resolution with economy. This is achieved by a technique that employs overlapping grids and b...

This preprint appeared firstly in Russian in 1997. Some truncated versions of this preprint were published in English and French, here a fully translated version is presented. The translation in English was done by O. V. Feodoritova and V. Deledicque to whom I express my gratitude. Key-words: Godunov’s Scheme, hyperbolic systems of conservation laws. ∗ Sobolev Institute of Mathematics, Novosibi...

generalized algorithm. The previous high order Godunov methods on which it is strongly based can be found in the A second-order Godunov method is proposed for the solution of general systems of conservation laws on arbitrary grids. Some original bibliography ([2, 4, 14, 15]) and in the book of applications are discussed: moving and deforming grids, local grid LeVecque [8]. refinement, Lagrangia...

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer–Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent ‘eddy diffusion’. W...

In these proceedings we present recent efforts to understand the energetics of magnetohydrodynamic (MHD) turbulence driven by the magneto-rotational instability (MRI). These studies are carried out in the local (shearing box) approximation using the Athena simulation code. Athena is a higher order Godunov algorithm based on the piecewise parabolic method (PPM), the corner transport upwind (CTU)...

Abstract The paper considers the numerical simulation of spatial flows real media in safety valves on basis problem an arbitrary discontinuity breakdown with complex equations state. solution is constructed by means developed method, which a modification classical scheme S. K. Godunov and includes various state matter. Van der Waals were used to model flow gases, Mie-Grüneisen equation was desc...