Create Presentation
Download Presentation

Download Presentation
## Solving linear systems in fluid dynamics

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Solving linear systems in fluid dynamics**P. Aaron Lott Applied Mathematics and Scientific Computation Program University of Maryland**Non-zero structure of 2D Poisson OperatorUsing a Spectral**Element Discretization**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**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**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**Opportunities/Resources**• Burgers Program in Fluid Dynamics • Center for Scientific Computation and Mathematical Modeling • AMSC Faculty Research Interests • AMSC Wiki (CFD)