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- P. F. Fischer
- 1997

Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompress-ible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the… (More)

High-order methods for incompressible fluid flow / M. Includes bibliographical references and index.

- James W. Lottes, Paul F. Fischer
- J. Sci. Comput.
- 2005

We study the performance of the multigrid method applied to spectral element (SE) discretizations of the Poisson and Helmholtz equations. Smoothers based on finite element (FE) discretizations, overlapping Schwarz methods, and point-Jacobi are considered in conjunction with conjugate gradient and GMRES acceleration techniques. It is found that Schwarz… (More)

- Paul F. Fischer, Gerald W. Kruse, Francis Loth
- J. Sci. Comput.
- 2002

We describe the development and implementation of an efficient spectral element code for simulating transitional flows in complex three-dimensional domains. Critical to this effort is the use of geometrically nonconforming elements that allow localized refinement in regions of interest, coupled with a stabilized high-order time-split formulation of the… (More)

Overflows are bottom gravity currents that supply dense water masses generated in high-latitude and marginal seas into the general circulation. Oceanic observations have revealed that mixing of overflows with ambient water masses takes place over small spatial and time scales. Studies with ocean general circulation models indicate that the strength of the… (More)

- Paul F Fischer
- 1993

Projection techniques are developed for computing approximate solutions to linear systems of the form Ax n = b n , for a sequence n = 1; 2; :::, e.g., arising from time discretization of a partial diierential equation. The approximate solutions are based upon previous solutions, and can be used as initial guesses for iterative solution of the system,… (More)

The performance of multigrid methods for the standard Poisson problem and for the consistent Poisson problem arising in spectral element discretizations of the Navier-Stokes equations is investigated. It is demonstrated that overlapping additive Schwarz methods are effective smoothers, provided that the solution in the overlap region is weighted by the… (More)

- Taehun Lee, Paul F Fischer
- Physical review. E, Statistical, nonlinear, and…
- 2006

A formulation of the intermolecular force in the nonideal-gas lattice Boltzmann equation method is examined. Discretization errors in the computation of the intermolecular force cause parasitic currents. These currents can be eliminated to roundoff if the potential form of the intermolecular force is used with compact isotropic discretization. Numerical… (More)

- Khosro Shahbazi, Paul F. Fischer, C. Ross Ethier
- J. Comput. Physics
- 2007

We present a high-order discontinuous Galerkin discretization of the unsteady in-compressible Navier-Stokes equations in convection-dominated flows using triangular and tetrahedral meshes. The scheme is based on a semi-explicit temporal discretization with explicit treatment of the nonlinear term and implicit treatment of the Stokes operator. The nonlinear… (More)

- Henry M. Tufo, Paul F. Fischer
- J. Parallel Distrib. Comput.
- 2001

We develop a fast direct solver for parallel solution of \coarse grid" problems, Ax = b, such as arise when domain decomposition or multigrid methods are applied to elliptic partial diierential equations in d space dimensions. The approach is based upon a (quasi-) sparse factorization of the inverse of A. If the dimension of the system is n and the number… (More)