Second-order Godunov-type scheme for reactive flow calculations on moving meshes

Abstract

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.

A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains

“…Among the techniques considered so far are elaborate moving mesh methods [5], dynamically adaptive overlapping structured meshes [6], boundaryaligned structured meshes [7], and purely Eulerian Cartesian methods that either use octree-based cell-wise refinement [8,9] or a patch-based approach with block-structured refinement grids [10,11,12,13]. In here, we focus on the latter adaptation methodology, originally proposed for non-reactive gas dynamics [14], since it promises greatest performance on the current generation of super-scalar computers.…”

Adaptive moving mesh methods for two-dimensional resistive magneto-hydrodynamic PDE models

“…The grids are moved continuously in the whole solution domain to cluster grid points in regions where the solution has the larger variations. In the past two decades this numerical technique has been proven very powerful for solving time-dependent problems whose solution has large gradient or discontinuities, see, e.g., [1,2,13,17,24,25,31]. We refer the readers to a recent interesting review paper [36] on moving mesh method for computational fluid dynamics and reference therein.…”

A method of constructing adaptive hexahedral moving grids

“…Those methods allow the execution of additional control for the cell shape by applying specific functionals. Description of some variational adaptive mesh methods and applications can be found, for instance, in the monographs [1][2][3][4][5][6], surveys [7][8][9][10][11], papers [12][13][14][15][16][17][18][19][20][21][22], and others. Generally, in the adaptive mesh approach, the equidistribution principle is employed for the error estimates of the solution or for geometrical parameters of the monitor surface.…”