4,582 research outputs found
Alternating-Direction Line-Relaxation Methods on Multicomputers
We study the multicom.puter performance of a three-dimensional Navier–Stokes solver based on alternating-direction line-relaxation methods. We compare several multicomputer implementations, each of which combines a particular line-relaxation method and a particular distributed block-tridiagonal solver. In our experiments, the problem size was determined by resolution requirements of the application. As a result, the granularity of the computations of our study is finer than is customary in the performance analysis of concurrent block-tridiagonal solvers. Our best results were obtained with a modified half-Gauss–Seidel line-relaxation method implemented by means of a new iterative block-tridiagonal solver that is developed here. Most computations were performed on the Intel Touchstone Delta, but we also used the Intel Paragon XP/S, the Parsytec SC-256, and the Fujitsu S-600 for comparison
Navier-Stokes simulation of wind-tunnel flow using LU-ADI factorization algorithm
The three dimensional Navier-Stokes solution code using the LU-ADI factorization algorithm was employed to simulate the workshop test cases of transonic flow past a wing model in a wind tunnel and in free air. The effect of the tunnel walls is well demonstrated by the present simulations. An Amdahl 1200 supercomputer having 128 Mbytes main memory was used for these computations
An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary
Common efficient schemes for the incompressible Navier-Stokes equations, such
as projection or fractional step methods, have limited temporal accuracy as a
result of matrix splitting errors, or introduce errors near the domain
boundaries (which destroy uniform convergence to the solution). In this paper
we recast the incompressible (constant density) Navier-Stokes equations (with
the velocity prescribed at the boundary) as an equivalent system, for the
primary variables velocity and pressure. We do this in the usual way away from
the boundaries, by replacing the incompressibility condition on the velocity by
a Poisson equation for the pressure. The key difference from the usual
approaches occurs at the boundaries, where we use boundary conditions that
unequivocally allow the pressure to be recovered from knowledge of the velocity
at any fixed time. This avoids the common difficulty of an, apparently,
over-determined Poisson problem. Since in this alternative formulation the
pressure can be accurately and efficiently recovered from the velocity, the
recast equations are ideal for numerical marching methods. The new system can
be discretized using a variety of methods, in principle to any desired order of
accuracy. In this work we illustrate the approach with a 2-D second order
finite difference scheme on a Cartesian grid, and devise an algorithm to solve
the equations on domains with curved (non-conforming) boundaries, including a
case with a non-trivial topology (a circular obstruction inside the domain).
This algorithm achieves second order accuracy (in L-infinity), for both the
velocity and the pressure. The scheme has a natural extension to 3-D.Comment: 50 pages, 14 figure
A compressible Navier-Stokes code for turbulent flow modeling
An implicit, finite volume code for solving two dimensional, compressible turbulent flows is described. Second order upwind differencing of the inviscid terms of the equations is used to enhance stability and accuracy. A diagonal form of the implicit algorithm is used to improve efficiency. Several zero and two equation turbulence models are incorporated to study their impact on overall flow modeling accuracy. Applications to external and internal flows are discussed
Numerical Simulation of Flow Through an Artificial Heart
A solution procedure was developed that solves the unsteady, incompressible Navier-Stokes equations, and was used to numerically simulate viscous incompressible flow through a model of the Pennsylvania State artificial heart. The solution algorithm is based on the artificial compressibility method, and uses flux-difference splitting to upwind the convective terms; a line-relaxation scheme is used to solve the equations. The time-accuracy of the method is obtained by iteratively solving the equations at each physical time step. The artificial heart geometry involves a piston-type action with a moving solid wall. A single H-grid is fit inside the heart chamber. The grid is continuously compressed and expanded with a constant number of grid points to accommodate the moving piston. The computational domain ends at the valve openings where nonreflective boundary conditions based on the method of characteristics are applied. Although a number of simplifing assumptions were made regarding the geometry, the computational results agreed reasonably well with an experimental picture. The computer time requirements for this flow simulation, however, are quite extensive. Computational study of this type of geometry would benefit greatly from improvements in computer hardware speed and algorithm efficiency enhancements
Spectral methods for CFD
One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched
Navier-Stokes calculations with a coupled strongly implicit method. Part 2: Spline solutions
A coupled strongly implicit method is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equation. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered. In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations
Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver
A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure
Recent update of the RPLUS2D/3D codes
The development of the RPLUS2D/3D codes is summarized. These codes utilize LU algorithms to solve chemical non-equilibrium flows in a body-fitted coordinate system. The motivation behind the development of these codes is the need to numerically predict chemical non-equilibrium flows for the National AeroSpace Plane Program. Recent improvements include vectorization method, blocking algorithms for geometric flexibility, out-of-core storage for large-size problems, and an LU-SW/UP combination for CPU-time efficiency and solution quality
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