Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions

For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit “time”-stepping applied to preconditioned Euler equations. The locally implicit iteration step is optimized for good damping of high-frequency errors. Numerical inaccuracy at low Mach numbers is also addressed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41714/1/10444_2005_Article_BF02123476.pd

Efficient upwind algorithms for solution of the Euler and Navier-stokes equations

An efficient three-dimensionasl tructured solver for the Euler and Navier-Stokese quations is developed based on a finite volume upwind algorithm using Roe fluxes. Multigrid and optimal smoothing multi-stage time stepping accelerate convergence. The accuracy of the new solver is demonstrated for inviscid flows in the range 0.675 :5M :5 25. A comparative grid convergence study for transonic turbulent flow about a wing is conducted with the present solver and a scalar dissipation central difference industrial design solver. The upwind solver demonstrates faster grid convergence than the central scheme, producing more consistent estimates of lift, drag and boundary layer parameters. In transonic viscous computations, the upwind scheme with convergence acceleration is over 20 times more efficient than without it. The ability of the upwind solver to compute viscous flows of comparable accuracy to scalar dissipation central schemes on grids of one-quarter the density make it a more accurate, cost effective alternative. In addition, an original convergencea cceleration method termed shock acceleration is proposed. The method is designed to reduce the errors caused by the shock wave singularity M -+ 1, based on a localized treatment of discontinuities. Acceleration models are formulated for an inhomogeneous PDE in one variable. Results for the Roe and Engquist-Osher schemes demonstrate an order of magnitude improvement in the rate of convergence. One of the acceleration models is extended to the quasi one-dimensiona Euler equations for duct flow. Results for this case d monstrate a marked increase in convergence with negligible loss in accuracy when the acceleration procedure is applied after the shock has settled in its final cell. Typically, the method saves up to 60% in computational expense. Significantly, the performance gain is entirely at the expense of the error modes associated with discrete shock structure. In view of the success achieved, further development of the method is proposed

Computational mechanics and physics at NASA Langley Research Center

An overview is given of computational mechanics and physics at NASA Langley Research Center. Computational analysis is a major component and tool in many of Langley's diverse research disciplines, as well as in the interdisciplinary research. Examples are given for algorithm development and advanced applications in aerodynamics, transition to turbulence and turbulence simulation, hypersonics, structures, and interdisciplinary optimization

Improving Euler computations at low Mach numbers

The paper consists of two parts, both dealing with conditioning techniques for lowMach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is investigated. Error decay by convection over domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit "time" stepping applied to preconditioned Euler equations. The locally implicit iteration step is optimized for good damping of high-frequency errors. Numerical inaccuracy at low Mach numbers is also addressed. In the present case it is not necessary to solve this accuracy problem. In the second part, insight is given in the conditions of derivative matrices to be inverted in point-relaxation methods for 1-D and 2-D, upwind-discretized Euler equations. Speed regimes are found where ill-conditioning of these matrices occurs, 1-D flow equations appear to be less well conditioned than 2-D flow equations. Fixes to the ill conditions follow more or less directly, when thinking of adding regularizing matrices to the ill-conditioned derivative matrices. A smoothing analysis is made of point Gauss-Seidel relaxation applied to Euler equations conditioned by such an additive matrix. The method is successfully applied to a very low-subsonic, steady, 2-D stagnation flow

A local Navier-Stokes preconditioner for all Mach and cell Reynolds numbers

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76362/1/AIAA-1997-2024-526.pd

Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated

Thermodynamic Conditions in Quenching Chamber of Low Voltage Circuit Breaker

Práce se zabývá studiem procesů probíhajících při zhášení silnoproudého oblouku ve zhášecí komoře jističe. Je zaměřena na výpočet dynamiky tekutin a teplotního pole v okolí elektrického oblouku. V práci je dále popsán vliv vzdálenosti plechů v komoře a vliv tvarů plechů z hlediska aerodynamických podmínek uvnitř komory. Dalším cílem dosaženým touto prací je poskytnutí informací o vlivu polohy elektrického oblouku na termodynamické vlastnosti uvnitř komory. Toto je důležité, zejména pokud je oblouk do komory vtahován jinými silami, např. elektromagnetickými a během tohoto vtahovacího procesu mění svůj tvar i polohu. Za účelem co nejjednoduššího, ale zároveň co nejefektivnějšího řešení úkolu, byl vyvinut software určen speciálně pro výpočet dynamiky tekutin numerickou metodou konečných objemů (FVM). Tato metoda je, v porovnání s rozšířenější metodou konečných prvků (FEM), vhodnější pro výpočet dynamiky tekutin (CFD) zejména proto, že režie na výpočet jedné iterace jsou menší v porovnání s ostatními numerickými metodami. Další výhodou tohoto softwarového řešení je jeho modularita a rozšiřitelnost. Cely koncept softwaru je postaven na tzv. zásuvných modulech. Díky tomuto řešení můžeme využít výpočtové jádro pro další numerické analýzy, např. strukturální, elektromagnetickou apod. Jediná potřeba pro úspěšné používání těchto analýz je napsáni solveru pro konečné prvky (FEM). Jelikož je software koncipován jako multi–thread aplikace, využívá výkon současných vícejádrových procesorů naplno. Tato vlastnost se ještě více projeví, pokud se výpočet přesune z CPU na GPU. Jelikož současné grafické karty vyšších tříd mají několik desítek až stovek výpočetních jader a pracují s mnohem rychlejšími pamětmi, než CPU, je výpočetní výkon několikanásobně vyšší.Work deals with the study of processes that attend the electric arc extinction inside the quenching chamber of a circuit breaker. It is focused on several areas. The first one is concerned to fluid dynamics calculations (CFD) and the second one is aimed at thermal field calculations. In this work effects of metal plates distance together with metal plates shapes are described from aerodynamical point of view. Another objective solved by this work is to give information about influence of an electric arc position in a quenching chamber, which changed its shape due to forces acting on it during extinction process. For purpose of this work a new software solution for CFD was developed. Whole software concept is based on plug-ins. Due to this solution, the software§s calculation core can be used for other numerical analyses, like structural, electromagnetic, etc. The only requirement is to write a plug-in for these analyses. Because the software is designed as multi-threaded application, it can use the fully performance of current multi-core processors. Above mentioned property can be especially shown off, when a calculation is moved from CPU to GPU (Graphics Processing Units). Current high-end graphic cards have tens to hundreds cores and work with faster memories than CPU. Due to this fact, the simulation performance can raised manifold.

Comparison of Several Dissipation Algorithms for Central Difference Schemes

Several algorithms for introducing artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme