Meros: Software for Block Preconditioning the Navier-Stokes Equations

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Presentation transcript:

Meros: Software for Block Preconditioning the Navier-Stokes Equations Robert Shuttleworth (CSCAMM/AMSC) Howard Elman (CS/AMSC) Vicki Howle, John Shadid, and Ray Tuminaro (Sandia National Labs) Motivation: Develop fully implicit solution methods to the incompressible Navier-Stokes Efficient, robust solution of flow problems requires block preconditioning Linear Solvers: Operator Based Block Preconditioning Focus: Adapt block preconditioners to the linear subproblems that arise in realistic fluid flow problems MPSalsa: Realistic, massively parallel, chemically reactive fluid flow code 11/12/2018 SC Student Seminar

Introduction Given the Navier-Stokes Equations: Nonlinear Term: Oseen: Newton: Jacobian of Momentum Eq. Discretization and Linearization: Vectors, example sizes, sparsity, computation gets expensive because … 11/12/2018 SC Student Seminar

Where Meros fits Packages: Nonlinear Solver Linear block precondition Methods Component Nonlinear Solver Linear block precondition MPSalsa Meros Newton-Krylov Finite Element GMRESR Time Loop Nonlinear Loop Linear Solver Block Precond End NonLin Loop End Time Loop 11/12/2018 SC Student Seminar

Block Preconditioners Discretization Consider: Optimal preconditioner is when X is the Schur Complement, Question: How to approximate the Schur complement? 11/12/2018 SC Student Seminar

MPSalsa Steady Problem Results Mesh Size Incomplete LU Fp 10 64 x 64 88.0 25.4 128 x 128 194.2 23.2 100 95.7 40.8 335.3 40.7 200 95.9 56.6 364.7 53.7 Challenges in mpsalsa, salsa uses stabilization, less control over discretization, salsa supplied fp, ap from salsa, issues, fp mesh indy not ilut, issue with parallelize Mesh Refinement Results – 2D Lid Driven Cavity The values in each column represent the average number of Outer Saddle Point Solves per Newton Step. 11/12/2018 SC Student Seminar

MPSalsa Steady Problem Results The Fp preconditioner converges in less computational time than ILU on a lid driven cavity problem with 200,000 unknowns. This graph represents the average number of linear iterations per nonlinear step for the 2D lid driven cavity problem with 12,000 unknowns. 11/12/2018 SC Student Seminar

Future Work Parallel Trials More intricate flow problems 512 Dual Node Sandia Linux Cluster Sandia’s ASCI Red Supercomputer Sandia’s ASCI Red Storm Supercomputer More intricate flow problems Backward facing step Diamond obstruction Chemically reactive flow 11/12/2018 SC Student Seminar