1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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