Search NASA⌕ Search

SEARCH · Search NASA

Results for “Poisson solver algorithm”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

22 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A dual potential formulation of the Navier-Stokes equations

A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented. The velocity field is decomposed using a scalar and vector potential. Vorticity and dilatation are used as the dependent variables in the momentum equations. Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations. A three-dimensional incompressible flow formulation is also described. An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential). The Helmholtz decomposition theorem allows this splitting of the velocity field. This approach has had only limited use since it increases the number of dependent variables in the solution. However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate. This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity. A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations. Several levels of flow approximation are available within the framework of this method. Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation. Solution efficiency can be enhanced in a straightforward way. For some flows, the vorticity and/or dilatation may be negligible in certain regions (e.g., far from a viscous boundary in an external flow). It is possible to drop the calculation of these variables then and optimize the solution speed. Also, efficient Poisson solvers are available for the potentials. The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed.

Gegg, S. G.↗
NASA NTRS1996

MGLab: An Interactive Multigrid Environment

MGLab is a set of Matlab functions that defines an interactive environment for experimenting with multigrid algorithms. The package solves two-dimensional elliptic partial differential equations discretized using either finite differences or finite volumes, depending on the problem. Built-in problems include the Poisson equation, the Helmholtz equation, a convection-diffusion problem, and a discontinuous coefficient problem. A number of parameters controlling the multigrid V-cycle can be set using a point-and-click mechanism. The menu-based user interface also allows a choice of several Krylov subspace methods, including CG, GMRES(k), and Bi-CGSTAB, which can be used either as stand-alone solvers or as multigrid acceleration schemes. The package exploits Matlab's visualization and sparse matrix features and has been structured to be easily extensible.

Bordner, James↗
NASA NTRS1993

Implementing abstract multigrid or multilevel methods

Multigrid methods can be formulated as an algorithm for an abstract problem that is independent of the partial differential equation, domain, and discretization method. In such an abstract setting, problems not arising from partial differential equations can be treated. A general theory exists for linear problems. The general theory was motivated by a series of abstract solvers (Madpack). The latest version was motivated by the theory. Madpack now allows for a wide variety of iterative and direct solvers, preconditioners, and interpolation and projection schemes, including user callback ones. It allows for sparse, dense, and stencil matrices. Mildly nonlinear problems can be handled. Also, there is a fast, multigrid Poisson solver (two and three dimensions). The type of solvers and design decisions (including language, data structures, external library support, and callbacks) are discussed. Based on the author's experiences with two versions of Madpack, a better approach is proposed. This is based on a mixed language formulation (C and FORTRAN + preprocessor). Reasons for not using FORTRAN, C, or C++ (individually) are given. Implementing the proposed strategy is not difficult.

Douglas, Craig C.↗
NASA NTRS1995

A comparison of two algorithms for simulating collisionless systems

Two completely different simulation algorithms are compared by applying them to the same stellar dynamical problems: one is a self-consistent field (SCF) method for solving Poisson's equation and the other is a phase-space method for integrating the collisionless Boltzmann equation. We consider simulations of spherical stellar systems which are initially far from equilibrium and relax to their final states by gravitational collapse. The initial conditions consist of either uniform-density spheres or nonequilibrium models having Plummer density profiles, in which velocity dispersions are assigned according to given virial ratios. If a few tens of radial expansion terms with hundreds of thousands of particles are used in the SCF code, excellent agreement is found between the results it generates and those obtained with the phase-space solver, provided that a sufficiently large number of grid cells are employed with the latter. These findings imply that for simulating collisionless systmes over many dynamical times, the SCF approach based on sampling phase space is competitive with the approach treating phase space as a continuous fluid. The results of our tests make it possible to estimate the number of particles and basis functions required in situations like those modeled. Limitations of the SCF method and the choice of an optimal set of basis functions are also discussed.

Hozumi, Shunsuke↗