Parallel Anisotropic Block-based Adaptive Mesh Refinement Algorithm For Three-dimensional Flows

A three-dimensional, parallel, anisotropic, block-based, adaptive mesh refinement (AMR) algorithm is proposed and described for the solution of fluid flows on body-fitted, multi-block, hexahedral meshes. Refinement and de-refinement in any grid block computational direction, or combination of directions, allows the mesh to rapidly adapt to anisotropic flow features such as shocks, boundary layers, or flame fronts, common to complex flow physics. Anisotropic refinements and an efficient and highly scalable parallel implementation lead to a potential for significant reduction in computational cost as compared to a more typical isotropic approach. Unstructured root-block topology allows for greater flexibility in the treatment of complex geometries. The AMR algorithm is coupled with an upwind finite-volume scheme for the solution of the Euler equations governing inviscid, compressible, gaseous flow. Steady-state and time varying, three-dimensional, flow problems are investigated for various geometries, including the cubed-sphere mesh.%%%%MAST

[1]  Quentin F. Stout,et al.  Adaptive Blocks: A High Performance Data Structure , 1997, SC.

[2]  Jason Zx Zheng,et al.  Block-based Adaptive Mesh Refinement Finite-volume Scheme for Hybrid Multi-block Meshes , 2012 .

[3]  Bram van Leer,et al.  Design of Optimally Smoothing Multi-Stage Schemes for the Euler Equations , 1989 .

[4]  Clinton P. T. Groth,et al.  Parallel High-Order Anisotropic Block-Based Adaptive Mesh Refinement Finite-Volume Scheme , 2011 .

[5]  Clinton P. T. Groth,et al.  Parallel Adaptive Mesh Refinement Scheme for Three-Dimensional Turbulent Non-Premixed Combustion , 2008 .

[7]  D. Venditti,et al.  Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows , 2003 .

[8]  Lucian Ivan,et al.  Development of High-order CENO Finite-volume Schemes with Block-based Adaptive Mesh Refinement (AMR) , 2011 .

[9]  W. Henshaw,et al.  Composite overlapping meshes for the solution of partial differential equations , 1990 .

[10]  Darren L. de Zeeuw.  A quadtree-based adaptively-refined Cartesian-grid algorithm for solution of the Euler equations , 1993 .

[11]  N. Hariharan,et al.  A 2 exp n tree based automated viscous Cartesian grid methodology for feature capturing , 1999 .

[12]  Gediminas Adomavicius,et al.  A Parallel Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries , 2000 .

[13]  Quentin F. Stout,et al.  A parallel solution-adaptive scheme for ideal magnetohydrodynamics , 1999 .

[14]  Rolf Rannacher,et al.  A Priori Error Estimates for the Finite Element Discretization of Elliptic Parameter Identification Problems with Pointwise Measurements , 2005, SIAM J. Control. Optim..

[15]  Clinton P. T. Groth,et al.  A parallel solution - adaptive method for three-dimensional turbulent non-premixed combusting flows , 2010, J. Comput. Phys..

[16]  P. Paolucci,et al.  The “Cubed Sphere” , 1996 .

[17]  C. Angelopoulos.  High resolution schemes for hyperbolic conservation laws , 1992 .

[18]  Clinton P. T. Groth,et al.  Assessment of Riemann solvers for unsteady one-dimensional inviscid flows for perfect gases , 1988 .

[19]  Xinfeng Gao,et al.  A Parallel Solution-Adaptive Method for Turbulent Non-Premixed Combusting Flows , 2008 .

[20]  Marsha J. Berger,et al.  AMR on the CM-2 , 1994 .

[21]  William D. Henshaw,et al.  Adaptive Mesh Refinement on Overlapping Grids , 2005 .

[22]  Michael J. Aftosmis,et al.  Robust and efficient Cartesian mesh generation for component-based geometry , 1997 .

[23]  D. D. Zeeuw,et al.  Global three‐dimensional MHD simulation of a space weather event: CME formation, interplanetary propagation, and interaction with the magnetosphere , 2000 .

[24]  D. Venditti,et al.  Adjoint error estimation and grid adaptation for functional outputs: application to quasi-one-dimensional flow , 2000 .

[25]  W. Coirier.  An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ. , 1994 .

[26]  Timothy J. Barth,et al.  Recent developments in high order K-exact reconstruction on unstructured meshes , 1993 .

[27]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[28]  Clinton P. T. Groth,et al.  A computational framework for predicting laminar reactive flows with soot formation , 2010 .

[29]  Jenmy Zimi Zhang.  Parallel Anisotropic Block-based Adaptive Mesh Refinement Finite-volume Scheme , 2012 .

[30]  D. D. Zeeuw,et al.  An adaptively refined Cartesian mesh solver for the Euler equations , 1993 .

[31]  Zhi J. Wang,et al.  Anisotropic Solution-Adaptive Viscous Cartesian Grid Method for Turbulent Flow Simulation , 2002 .

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

[33]  David L. Darmofal,et al.  Anisotropic Adaptation for Functional Outputs of Viscous Flow Simulations , 2003 .

[34]  James J. Quirk,et al.  A Parallel Adaptive Mesh Refinement Algorithm , 1993 .

[35]  Gianluca Iaccarino,et al.  LES on Cartesian Grids with Anisotropic Refinement , 2007 .

[36]  Philip L. Roe,et al.  Adaptive-mesh algorithms for computational fluid dynamics , 1993 .

[37]  D. Venditti,et al.  Grid adaptation for functional outputs: application to two-dimensional inviscid flows , 2002 .

[38]  Domenic D'Ambrosio,et al.  Upwind methods and carbuncle phenomenon , 1998 .

[39]  T. Linde,et al.  A practical, general‐purpose, two‐state HLL Riemann solver for hyperbolic conservation laws , 2002 .

[40]  Henri Paillere,et al.  A wave-model-based refinement criterion for adaptive-grid computation of compressible flows , 1992 .

[41]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[42]  Clinton P. T. Groth,et al.  PARALLEL SOLUTION-ADAPTIVE SCHEME FOR MULTI-PHASE CORE FLOWS IN ROCKET MOTORS , 2003 .

[43]  Clinton P. T. Groth,et al.  Solution of the equation of radiative transfer using a Newton-Krylov approach and adaptive mesh refinement , 2012, J. Comput. Phys..

[44]  P. Lax,et al.  On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[45]  Scott Northrup,et al.  Solution of Laminar Diffusion Flames Using a Parallel Adaptive Mesh Refinement Algorithm , 2005 .

[46]  Scott Northrup,et al.  Parallel Implicit Adaptive Mesh Refinement Scheme for Body-Fitted Multi-Block Mesh , 2005 .

[47]  Clinton P. T. Groth,et al.  High-Order Central ENO Finite-Volume Scheme with Adaptive Mesh Refinement , 2007 .

[48]  Clinton P. T. Groth,et al.  3D multi‐fluid MHD studies of the solar wind interaction with Mars , 1999 .

[49]  K. Powell,et al.  Magnetospheric configuration for Parker-spiral IMF conditions: Results of a 3D AMR MHD simulation , 2000 .

[50]  Clinton P. T. Groth,et al.  International Journal of Computational Fluid Dynamics a Parallel Adaptive Mesh Refinement Algorithm for Predicting Turbulent Non-premixed Combusting Flows a Parallel Adaptive Mesh Refinement Algorithm for Predicting Turbulent Non-premixed Combusting Flows , 2022 .

[51]  Ch. Hirsch,et al.  Fundamentals Of Computational Fluid Dynamics , 2016 .

[52]  Hans De Sterck,et al.  Hyperbolic Conservation Laws on Three-Dimensional Cubed-Sphere Grids : A Parallel Solution-Adaptive Simulation Framework , 2012 .

[53]  J. Sachdev,et al.  A parallel solution-adaptive scheme for multi-phase core flows in solid propellant rocket motors , 2005 .

[54]  Rony Keppens,et al.  Hybrid block-AMR in cartesian and curvilinear coordinates: MHD applications , 2007, J. Comput. Phys..

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

[56]  Fue-Sang Lien,et al.  A Cartesian Grid Method with Transient Anisotropic Adaptation , 2002 .

[57]  Clinton P. T. Groth,et al.  Numerical Modeling of Micron-Scale Flows Using the Gaussian Moment Closure , 2005 .

[58]  Lucian Ivan,et al.  Three-Dimensional MHD on Cubed-Sphere Grids: Parallel Solution-Adaptive Simulation Framework , 2011 .

[59]  V. Venkatakrishnan.  On the accuracy of limiters and convergence to steady state solutions , 1993 .

[60]  C. P. T. Groth,et al.  A Parallel Adaptive 3D MHD Scheme for Modeling Coronal and Solar Wind Plasma Flows , 1999 .

[61]  Marsha Berger,et al.  Data structures for adaptive grid generation , 1986 .

[62]  R. LeVeque,et al.  An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries , 1989 .

[63]  Scott Northrup,et al.  Parallel solution-adaptive method for two dimensional non-premixed combusting flows , 2011 .

[64]  J. Hansen,et al.  Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations , 1991 .

[65]  D. L. De Zeeuw,et al.  Three-dimensional mhd simulation of coronal mass ejections , 2000 .

[66]  Kristi D. Brislawn,et al.  Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolic conservation laws , 1995 .

[67]  I. Bohachevsky,et al.  Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .

[68]  Clinton P. T. Groth,et al.  A Mesh Adjustment Scheme for Embedded Boundaries , 2006 .

[69]  Rolf Rannacher,et al.  Duality-based adaptivity in the hp-finite element method , 2003, J. Num. Math..