Journal ArticleDOI
The bid method for the steady-state Navier-Stokes equations
Patrick J. Roache,Molly A. Ellis +1 more
TLDR
The Biharmonic Driver (BID) method as mentioned in this paper uses direct (non-iterative) linear biharmonic solvers to obtain solutions to the nonlinear two-dimensional steady-state incompressible Navier-Stokes equations.Citations
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Journal ArticleDOI
Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem
TL;DR: In this paper, the first bi-harmonic problem on general two-dimensional domains was solved using a mixed finite element method, where the continuous problem has been approximated by an appropriate mixed-finite element method.
Book ChapterDOI
Numerical experiments with a multiple grid and a preconditioned Lanczos type method
P. Wesseling,P. Sonneveld +1 more
Journal ArticleDOI
Projection conditions on the vorticity in viscous incompressible flows
L. Quartapelle,F. Valz-Gris +1 more
TL;DR: In this article, it was shown that the boundary conditions on the velocity imply conditions of an integral type on the vorticity, and that these conditions determine a projection of the VOR on the linear manifold of the harmonic vector fields.
Journal ArticleDOI
Vorticity conditioning in the computation of two-dimensional viscous flows
TL;DR: In this article, it is shown that the splitting of the fourth-order equation for the stream function into two second-order problems implies specific integral conditions which fix the abstract projection of the vorticity field with respect, to the linear manifold of the harmonic functions.
Journal ArticleDOI
Time-Dependent viscous incompressible Navier-Stokes equations: the finite difference Galerkin formulation and streamfunction algorithms
John W. Goodrich,W. Y. Soh +1 more
TL;DR: The FDG method is extended to time dependent incompressible Navier-Stokes equations and shows to be the discrete analog of the continuum manipulations that lead to the fourth-order streamfunction equation.
References
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Journal ArticleDOI
The Direct Solution of the Biharmonic Equation on Rectangular Regions and the Poisson Equation on Irregular Regions
B. L. Buzbee,Fred W. Dorr +1 more
TL;DR: In this article, the authors used the direct method of matrix decomposition to formulate an effective numerical algorithm for the discrete biharmonic equation on a rectangular region and the discrete Poisson equation on an irregular region.
Journal ArticleDOI
Numerical solution of the viscous flow in the entrance region of parallel plates
TL;DR: In this article, the Navier-Stokes equations were quasilinearized and the resultant linear equations were then approximated by finite-difference formulas, which were judiciously selected in order for the coefficient matrix of the finitedifference equations to be diagonally dominant.
Journal ArticleDOI
Block five diagonal matrices and the fast numerical solution of the biharmonic equation
Louis Bauer,Edward L. Reiss +1 more
TL;DR: A factoring and block elimination method for the fast numerical solution of block five diagonal linear algebraic equations is described in this paper, and applications of the method are given for the numerical solution for several boundary value problems involving the bi- harmonic operator.
Journal ArticleDOI
The LAD, NOS and split NOS methods for the steady-state Navier-Stokes equations
TL;DR: In this paper, three iterative methods for numerically solving the steady-state Navier-Stokes equations are presented, i.e., the Laplacian Driver (LAD), the Numerical Oseen (NOS), and the Split NOS method.
Journal ArticleDOI
Fast direct numerical solution of the nonhomogeneous Cauchy-Riemann equations
Harvard Lomax,E. Dale Martin +1 more
TL;DR: In this paper, a fast direct Cauchy-Riemann solver was developed for solving the finite-difference equations representing systems of first-order elliptic partial differential equations in the form of the nonhomogeneous Cauché Riemann equations.