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Solving linear systems in fluid dynamics

Solving linear systems in fluid dynamics

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Solving linear systems in fluid dynamics

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  1. Solving linear systems in fluid dynamics P. Aaron Lott Applied Mathematics and Scientific Computation Program University of Maryland

  2. Non-zero structure of 2D Poisson OperatorUsing a Spectral Element Discretization

  3. Incompressible Navier Stokes Equations

  4. 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

  5. Preconditioning

  6. 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

  7. 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

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