An MPI parallel level-set algorithm for propagating front curvature dependent detonation shock fronts in complex geometries

• Published in: Combustion theory and modelling Vol. 17; no. 1; pp. 109 - 141
• Main Authors: Hernández, Alberto, Bdzil, John B., Stewart, D. Scott
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.02.2013
• Subjects: Algorithms; computational physics; detonation shock dynamics; level sets; parallel computing; reactive flow
• ISSN: 1364-7830; 1741-3559
• DOI: 10.1080/13647830.2012.725579

We present a parallel, two-dimensional, grid-based algorithm for solving a level-set function PDE that arises in Detonation Shock Dynamics (DSD). In the DSD limit, the detonation shock propagates at a speed that is a function of the curvature of the shock surface, subject to a set of boundary conditions applied along the boundaries of the detonating explosive. Our method solves for the full level-set function field, φ(x, y, t), that locates the detonation shock with a modified level-set function PDE that continuously renormalises the level-set function to a distance function based off of the locus of the shock surface, φ(x, y, t)=0. The boundary conditions are applied with ghost nodes that are sorted according to their connectivity to the interior explosive nodes. This allows the boundary conditions to be applied via a local, direct evaluation procedure. We give an extension of this boundary condition application method to three dimensions. Our parallel algorithm is based on a domain-decomposition model which uses the Message-Passing Interface (MPI) paradigm. The computational order of the full level-set algorithm, which is O(N 4 ), where N is the number of grid points along a coordinate line, makes an MPI-based algorithm an attractive alternative. This parallel model partitions the overall explosive domain into smaller sub-domains which in turn get mapped onto processors that are topologically arranged into a two-dimensional rectangular grid. A comparison of our numerical solution with an exact solution to the problem of a detonation rate stick shows that our numerical solution converges at better than first-order accuracy as measured by an L1-norm. This represents an improvement over the convergence properties of narrow-band level-set function solvers, whose convergence is limited to a floor set by the width of the narrow band. The efficiency of the narrow-band method is recovered by using our parallel model.