Meros: Software for Block Preconditioning the Navier-Stokes Equations

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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)

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Introduction
Given the Navier-Stokes Equations
Nonlinear Term Oseen Newton Jacobian of
Momentum Eq.
Discretization and Linearization
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Where Meros fits
Time Loop
Nonlinear Loop
Linear Solver
Block Precond
End NonLin Loop
End Time Loop
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Block Preconditioners

• Discretization
• Consider
• Optimal preconditioner is when X is the Schur
  Complement,
• Question How to approximate the Schur
  complement?

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MPSalsa Steady Problem Results
Re Mesh Size Incomplete LU Fp
10 64 x 64 88.0 25.4
10 128 x 128 194.2 23.2
100 64 x 64 95.7 40.8
100 128 x 128 335.3 40.7
200 64 x 64 95.9 56.6
200 128 x 128 364.7 53.7
Mesh Refinement Results 2D Lid Driven Cavity
The values in each column represent the average
number of Outer Saddle Point Solves per Newton
Step.
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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.
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Future Work

• Parallel Trials
• 512 Dual Node Sandia Linux Cluster
• Sandias ASCI Red Supercomputer
• Sandias ASCI Red Storm Supercomputer
• More intricate flow problems
• Backward facing step
• Diamond obstruction
• Chemically reactive flow