Numerical simulation of detonation using an adaptive Cartesian cut-cell method combined with a cell-merging technique

A second-order accurate scheme for the Cartesian cut-cell method developed previously by the authors [Ji H, Lien F-S, Yee E. Comput. Methods Appl. Mech. Eng. 198 (2008), 432] is generalized for application to both two- and three-dimensional inviscid compressible flow problems. A cell-merging approach is used to address the so-called “small cell” problem that has plagued Cartesian cut-cell methods. In the present cell-merging approach, the conservative variables are stored at the cut-cell centroid (including the non-merged and merged cut-cells) rather than at the Cartesian cell center. Although this approach results in a more complicated search algorithm for the determination of the neighbor cells (required for the computation of the spatial gradients of the conservative variables), this approach enables the straightforward formulation of a higher than first-order accurate discretization scheme in the vicinity of the (complex and irregular) internal boundaries of the flow domain. Six test cases (including detonation problems) are used to demonstrate the accuracy and capability of the adaptive cut-cell method, for which both mesh refinement and derefinement techniques are employed in the case of an unsteady shock diffraction problem.