Solving linear systems in fluid dynamics

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Solving linear systems in fluid dynamics

• P. Aaron Lott
• Applied Mathematics and Scientific Computation
  Program
• University of Maryland

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Non-zero structure of 2D Poisson OperatorUsing a
Spectral Element Discretization
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Incompressible Navier Stokes Equations
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Discretized Steady Navier Stokes

• Each time step requires a Nonlinear Solve
• Each Nonlinear Solve requires a Linear solve
• Each Linear Solve can be expensive - Need
  efficient scalable solvers

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Preconditioning
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Preconditioner for Steady Navier Stokes Equations

• Choose P_F as an inexpensive approximation to F
• Choose P_S as an inexpensive approximation to the
  Schur complement of the system matrix

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References

• High-Order Methods for Incompressible Fluid Flow.
  Deville Fischer and Mund
• Spectral/hp Element Methods for Computational
  Fluid Dynamics. Karniadakis and Sherwin
• Spectral Methods Fundamentals in Single Domains.
  Canuto Hussaini Quarteroni Zang
• Finite Element Methods and Fast Iterative Solvers
  with applications in incompressible fluid
  dynamics. Elman Silverster and Wathen
• Iterative Methods for Sparse Linear Systems. Saad

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Opportunities/Resources

• Burgers Program in Fluid Dynamics
• Center for Scientific Computation and
  Mathematical Modeling
• AMSC Faculty Research Interests
• AMSC Wiki (CFD)