An adaptive multilevel local defect correction technique with application to combustion

The standard local defect correction (LDC) method has been extended to include multilevel adaptive gridding, domain decomposition and regridding. The domain decomposition algorithm provides a natural route for parallelization by employing many small tensor-product grids, rather than a single large unstructured grid; this algorithm can greatly reduce memory usage. The above properties are illustrated by successfully applying the new algorithm to a simple heat transfer problem with an analytical solution, and by subsequently solving the more complex problem of an axisymmetric laminar Bunsen flame with one-step chemistry. The simulation data show excellent agreement with results previously published in the literature.

[1]  Michael A. Heroux,et al.  Application of the fast adaptive composite grid method to computational fluid dynamics , 1986 .

[2]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[3]  J. Ferziger,et al.  An adaptive multigrid technique for the incompressible Navier-Stokes equations , 1989 .

[4]  P. Colella,et al.  A Fast Adaptive Vortex Method in Three Dimensions , 1994 .

[5]  Stephen F. McCormick,et al.  Multilevel adaptive methods for partial differential equations , 1989, Frontiers in applied mathematics.

[6]  M. Smooke,et al.  Error estimate for the modified Newton method with applications to the solution of nonlinear, two-point boundary-value problems , 1983 .

[7]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[8]  Pedro J. Coelho,et al.  Calculation of a Confined Axisymmetric Laminar Diffusion Flame Using a Local Grid Refinement Technique , 1993 .

[9]  Daniel F. Martin,et al.  A Cell-Centered Adaptive Projection Method for the Incompressible Euler Equations , 2000 .

[10]  William Gropp,et al.  Domain Decomposition with Local Mesh Refinement , 1992, SIAM J. Sci. Comput..

[11]  John B. Bell,et al.  An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion , 1998 .

[12]  Wolfgang Hackbusch,et al.  Local Defect Correction Method and Domain Decomposition Techniques , 1984 .

[13]  Joseph E. Flaherty,et al.  An adaptive local mesh refinement method for time-dependent partial differential equations , 1989 .

[14]  P. Vassilevski,et al.  Local refinement techniques for elliptic problems on cell-centered grids , 1991 .

[15]  de Hc Rick Lange,et al.  Numerical flow modelling in a locally refined grid , 1994 .

[16]  R.M.M. Mattheij,et al.  Local defect correction with different grid types , 2002 .

[17]  R. M. M. Mattheij,et al.  Convergence analysis of the local defect correction method for diffusion equations , 2003, Numerische Mathematik.

[18]  de Lph Philip Goey,et al.  A Numerical Study of a Premixed Flame on a Slit Burner , 1995 .

[19]  P. Vassilevski,et al.  Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis , 1991 .

[20]  R.M.M. Mattheij,et al.  Discretization of the stationary convection-diffusion-reaction equation , 1996 .

[21]  B. Bennett,et al.  Local rectangular refinement with application to axisymmetric laminar flames , 1998 .

[22]  Marsha Berger,et al.  Three-Dimensional Adaptive Mesh Refinement for Hyperbolic Conservation Laws , 1994, SIAM J. Sci. Comput..

[23]  P. Deuflhard.  A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting , 1974 .

[24]  Isidore Rigoutsos,et al.  An algorithm for point clustering and grid generation , 1991, IEEE Trans. Syst. Man Cybern..

[25]  S. McCormick,et al.  Fast Adaptive Composite Grid (FAC) Methods: Theory for the Variational Case , 1984 .

[26]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[27]  Pjj Peter Ferket.  Solving boundary value problems on composite grids with an application to combustion , 1996 .

[28]  Mjh Martijn Anthonissen.  Local defect correction techniques : analysis and application to combustion , 2001 .

[29]  Robert J. Kee,et al.  Solution of Premixed and Counterflow Diffusion Flame Problems by Adaptive Boundary Value Methods , 1985 .

[30]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[31]  Daniel F. Martin,et al.  Solving Poisson's Equation using Adaptive Mesh Renemen t , 1996 .

[32]  B. Bennett,et al.  Computational and experimental study of axisymmetric coflow partially premixed methane/air flames , 2000 .

[33]  S. McCormick,et al.  The fast adaptive composite grid (FAC) method for elliptic equation , 1986 .

[34]  B. Bennett,et al.  Local Rectangular Refinement with Application to Nonreacting and Reacting Fluid Flow Problems , 1999 .

[35]  Arnold Reusken,et al.  A finite difference discretization method for elliptic problems on composite grids , 2005, Computing.

[36]  Rolf Rannacher,et al.  Numerical simulation of laminar flames at low Mach number by adaptive finite elements , 1999 .

[37]  Marshall B. Long,et al.  A comparison of the structures of lean and rich axisymmetric laminar Bunsen flames: application of local rectangular refinement solution-adaptive gridding , 1999 .

[38]  M S Day,et al.  Numerical simulation of laminar reacting flows with complex chemistry , 2000 .

[39]  P. Colella,et al.  A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier-Stokes Equations , 1998 .

[40]  David E. Keyes,et al.  Towards Polyalgorithmic Linear System Solvers for Nonlinear Elliptic Problems , 1994, SIAM J. Sci. Comput..

[41]  A. J. Kotlar,et al.  The overall reaction concept in premixed, laminar, steady-state flames. II. Initial temperatures and pressures , 1984 .

[42]  Mitchell D. Smooke,et al.  The effect of overall discretization scheme on Jacobian structure, convergence rate, and solution accuracy within the local rectangular refinement method , 2001, Numer. Linear Algebra Appl..

[43]  P. Wesseling,et al.  Local Grid Refinement in Large-Eddy Simulation , 1997 .

[44]  Ulrich Rüde,et al.  A finite volume convergence theory for the fast adaptive composite grid methods , 1994 .