Theoretical and numerical structure for reacting shock waves
SIAM Journal on Scientific and Statistical Computing
The generalized Riemann problem for reactive flows
Journal of Computational Physics
Curvilinear grids of convex quadrilaterals
USSR Computational Mathematics and Mathematical Physics
Theoretical and numerical structure for unstable one-dimensional detonations
SIAM Journal on Applied Mathematics
Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
The construction of regular grids on n-dimensional surfaces
Computational Mathematics and Mathematical Physics
Numerical methods for hyperbolic conservation laws with stiff relaxation I: spurious solutions
SIAM Journal on Applied Mathematics
Error bounds for fractional step methods for conservation laws with source terms
SIAM Journal on Numerical Analysis
Improved shock-capturing methods for multicomponent and reacting flows
Journal of Computational Physics
Unsplit schemes for hyperbolic conservation laws with source terms in one space dimension
Journal of Computational Physics
A variational form of the Winslow grid generator
Journal of Computational Physics
The Convergence Rate of Finite Difference Schemes in the Presence of Shocks
SIAM Journal on Numerical Analysis
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
Reminiscences about difference schemes
Journal of Computational Physics
The random projection method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
Conditions of Nondegeneracy of Three-Dimensional Cells. A Formula of a Volume of Cells
SIAM Journal on Scientific Computing
A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
SIAM Journal on Scientific Computing
Variational Barrier Method of Adaptive Grid Generation in Hyperbolic Problems of Gas Dynamics
SIAM Journal on Numerical Analysis
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
Journal of Computational Physics
A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation
Journal of Computational Physics
Resolving the shock-induced combustion by an adaptive mesh redistribution method
Journal of Computational Physics
An adaptive mesh redistribution method for the incompressible mixture flows using phase-field model
Journal of Computational Physics
Journal of Computational Physics
Remapping-free ALE-type kinetic method for flow computations
Journal of Computational Physics
A Second-Order Accurate Conservative Front-Tracking Method in One Dimension
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Hi-index | 31.48 |
The method of calculating the system of gas dynamics equations coupled with the chemical reaction equation is considered. The flow parameters are updated in whole without splitting the system into a hydrodynamical part and an ODE part. The numerical algorithm is based on the Godunov's scheme on deforming meshes with some modification to increase the scheme-order in time and space. The variational approach is applied to generate the moving adaptive mesh. At every time step the functional of smoothness, written on the graph of the control function, is minimized. The grid-lines are condensed in the vicinity of the main solution singularities, e.g., precursor shock, fire zones, intensive transverse shocks, and slip lines, which allows resolving a fine structure of the reaction domain. The numerical examples relating to the Chapman-Jouguet detonation and unstable overdriven detonation are considered in both one and two space dimensions.