TY - JOUR

T1 - An MPI parallel level-set algorithm for propagating front curvature dependent detonation shock fronts in complex geometries

AU - Hernández, Alberto

AU - Bdzil, John B.

AU - Stewart, D. Scott

N1 - Funding Information:
We thank Tariq Aslam for discussions concerning the DSD boundary condition algorithm found in [6] and Michael Campbell and The University of Illinois Campus Cluster staff for their support on using Taub. The work was supported by grant and contract resources from the US Army Armament Research, Development and Engineering Center through UTRS, subcontract UTRS 09-292 and the US Air Force Research Laboratory, Munitions Directorate, Eglin AFB, FA865-05-1-0003.

PY - 2013/2

Y1 - 2013/2

N2 - 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(N4), 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.

AB - 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(N4), 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.

KW - computational physics

KW - detonation shock dynamics

KW - level sets

KW - parallel computing

KW - reactive flow

UR - http://www.scopus.com/inward/record.url?scp=84873903144&partnerID=8YFLogxK

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U2 - 10.1080/13647830.2012.725579

DO - 10.1080/13647830.2012.725579

M3 - Article

AN - SCOPUS:84873903144

SN - 1364-7830

VL - 17

SP - 109

EP - 141

JO - Combustion Theory and Modelling

JF - Combustion Theory and Modelling

IS - 1

ER -