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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Implicit upwind-Euler solution algorithms for unstructured-grid applications

The development of implicit upwind algorithms for the solution of the three-dimensional, time-dependent Euler equations on unstructured tetrahdral meshes is described. The implicit temporal discretization involves either a two-sweep Gauss-Seidel relaxation procedure, a two-sweep Point-Jacobi relaxation procedure, or a single-sweep Point-Implicit procedure; the upwind spatial discretization is based on the flux-difference splitting of Roe. Detailed descriptions of the three implicit solution algorithms are given, and calculations for the Boeing 747 transport configuration are presented to demonstrate the algorithms. Advantages and disadvantages of the implicit algorithms are discussed. A steady-state solution for the 747 configuration, obtained at transonic flow conditions using s mesh of over 100,000 cells, required less than one hour of CPU time on a Cray-2 computer, thus demonstrating the speed and robustness of the general capability.

Batina, John T.↗
NASA NTRS1984

An implicit form for the Osher upwind scheme

Conservative upwind schemes for the Euler equations, such as the Osher scheme, accurately resolve flow discontinuities and correctly model the physics of the problem. However, these schemes require many more arithmetic operations per integration step than simple central-difference schemes and hence result in large computing times. An implicit version of the first-order- and second-order-accurate Osher schemes in two spatial dimensions and generalized coordinates is developed in this study. Because implicit schemes permit the use of large integration steps, in many cases they require fewer integration steps to reach steady-state (especially in calculations on grids with widely varying mesh-cell sizes). The implicit scheme developed in this study accelerated convergence speeds by almost an order of magnitude in the problems considered. Test cases include quasi-one-dimensional nozzle flow and supersonic flow past a cylinder.

Rai, M. M.↗
NASA NTRS1998

Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes

Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach is developed which employs directional implicit smoothing with regular fully coarsened multigrid levels. The directional implicit smoothing is obtained by constructing implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergence rates over the traditional explicit full-coarsening multigrid algorithm. However, maximum benefits are achieved by combining the two approaches in a coupled manner into a single algorithm. An order of magnitude increase in convergence rate over the traditional explicit full-coarsening algorithm is demonstrated, and convergence rates for high-Reynolds number viscous flows which are independent of the grid aspect ratio are obtained. Further acceleration is provided by incorporating low-Mach-number preconditioning techniques, and a Newton-GMRES strategy which employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is documented through several example test cases.

Movriplis, Dimitri J.↗
NASA NTRS1982

A new numerical method for the simulation of three dimensional flow in a pipe

A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction.

Leonard, A.↗
NASA NTRS1982

A new numerical method for the simulation of three-dimensional flow in a pipe

A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction. Previously announced in STAR as N82-31644

Leonard, A.↗
NASA NTRS1986

Mathematical model for the Bridgman-Stockbarger crystal growing system

In a major technical breakthrough, a computer model for Bridgman-Stockbarger crystal growth was developed. The model includes melt convection, solute effects, thermal conduction in the ampule, melt, and crystal, and the determination of the curved moving crystal-melt interface. The key to the numerical method is the use of a nonuniform computational mesh which moves with the interface, so that the interface is a mesh surface. In addition, implicit methods are used for advection and diffusion of heat, concentration, and vorticity, for interface movement, and for internal gracity waves. This allows large time-steps without loss of stability or accuracy. Numerical results are presented for the interface shape, temperature distribution, and concentration distribution, in steady-state crystl growth. Solutions are presented for two test cases using water, with two different salts in solution. The two diffusivities differ by a factor of ten, and the concentrations differ by a factor of twenty.

Roberts, G. O.↗
NASA NTRS1988

Analysis of electrophoresis performance

A flexible efficient computer code is being developed to simulate electrophoretic separation phenomena, in either a cylindrical or a rectangular geometry. The code will computer the evolution in time of the concentrations of an arbitrary number of chemical species, and of the temperature, pH distribution, conductivity, electric field, and fluid motion. Use of nonuniform meshes and fast accurate implicit time-stepping will yield accurate answers at economical cost.

Roberts, Glyn O.↗
NASA NTRS1989

Numerical simulations in combustion

This paper reviews numerical simulations in reacting flows in general and combustion phenomena in particular. It is shown that use of implicit schemes and/or adaptive mesh strategies can improve convergence, stability, and accuracy of the solution. Difficulties increase as turbulence and multidimensions are considered, particularly when finite-rate chemistry governs the given combustion problem. Particular attention is given to the areas of solid-propellant combustion dynamics, turbulent diffusion flames, and spray droplet vaporization.

Chung, T. J.↗
NASA NTRS1991

Numerical simulation of the reactive flow in advanced (HSR) combustors using KIVA-2

Recent work has been done with the goal of establishing ultralow emission aircraft gas turbine combustors. A significant portion of the effort is the development of three dimensional computational combustor models. The KIVA-II computer code which is based on the Implicit Continuous Eulerian Difference mesh Arbitrary Lagrangian Eulerian (ICED-ALE) numerical scheme is one of the codes selected by NASA to achieve these goals. This report involves a simulation of jet injection through slanted slots within the Rich burn/Quick quench/Lean burn (RQL) baseline experimental rig. The RQL combustor distinguishes three regions of combustion. This work specifically focuses on modeling the quick quench mixer region in which secondary injection air is introduced radially through 12 equally spaced slots around the mixer circumference. Steady state solutions are achieved with modifications to the KIVA-II program. Work currently underway will evaluate thermal mixing as a function of injection air velocity and angle of inclination of the slots.

Winowich, Nicholas S.↗
NASA NTRS1993

A solution-adaptive hybrid-grid method for the unsteady analysis of turbomachinery

A solution-adaptive method for the time-accurate analysis of two-dimensional flows in turbomachinery is described. The method employs a hybrid structured-unstructured zonal grid topology in conjunction with appropriate modeling equations and solution techniques in each zone. The viscous flow region in the immediate vicinity of the airfoils is resolved on structured O-type grids while the rest of the domain is discretized using an unstructured mesh of triangular cells. Implicit, third-order accurate, upwind solutions of the Navier-Stokes equations are obtained in the inner regions. In the outer regions, the Euler equations are solved using an explicit upwind scheme that incorporates a second-order reconstruction procedure. An efficient and robust grid adaptation strategy, including both grid refinement and coarsening capabilities, is developed for the unstructured grid regions. Grid adaptation is also employed to facilitate information transfer at the interfaces between unstructured grids in relative motion. Results for grid adaptation to various features pertinent to turbomachinery flows are presented. Good comparisons between the present results and experimental measurements and earlier structured-grid results are obtained.

Mathur, Sanjay R.↗
NASA NTRS1997

CFD Analysis and Design Optimization Using Parallel Computers

A versatile and efficient multi-block method is presented for the simulation of both steady and unsteady flow, as well as aerodynamic design optimization of complete aircraft configurations. The compressible Euler and Reynolds Averaged Navier-Stokes (RANS) equations are discretized using a high resolution scheme on body-fitted structured meshes. An efficient multigrid implicit scheme is implemented for time-accurate flow calculations. Optimum aerodynamic shape design is achieved at very low cost using an adjoint formulation. The method is implemented on parallel computing systems using the MPI message passing interface standard to ensure portability. The results demonstrate that, by combining highly efficient algorithms with parallel computing, it is possible to perform detailed steady and unsteady analysis as well as automatic design for complex configurations using the present generation of parallel computers.

Martinelli, Luigi↗
NASA NTRS1998

Three-Dimensional High-Lift Analysis Using a Parallel Unstructured Multigrid Solver

A directional implicit unstructured agglomeration multigrid solver is ported to shared and distributed memory massively parallel machines using the explicit domain-decomposition and message-passing approach. Because the algorithm operates on local implicit lines in the unstructured mesh, special care is required in partitioning the problem for parallel computing. A weighted partitioning strategy is described which avoids breaking the implicit lines across processor boundaries, while incurring minimal additional communication overhead. Good scalability is demonstrated on a 128 processor SGI Origin 2000 machine and on a 512 processor CRAY T3E machine for reasonably fine grids. The feasibility of performing large-scale unstructured grid calculations with the parallel multigrid algorithm is demonstrated by computing the flow over a partial-span flap wing high-lift geometry on a highly resolved grid of 13.5 million points in approximately 4 hours of wall clock time on the CRAY T3E.

Mavriplis, Dimitri J.↗
NASA NTRS1994

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a multiple-instruction/multiple-data stream parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed: one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All of the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the Intel iPSC/860.

TRT-THEORETICAL↗
NASA NTRS1994

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on an MIMD (multiple instruction/multiple data stream) parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed, one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the iPSC/860.

Venkatakrishnan, V.↗
NASA NTRS1991

Modified ICED-ALE method for astrogeophysical plasma flows

The Implicit-Continuous-Eulerian-Difference Mesh-Arbitrary-Lagrangian-Eulerian (ICED-ALE) algorithm of Brackbill and Pracht (1973) is modified for the study of astrophysical plasma flows in which dynamical effects are important. In the present study the general-energy-conservation law is directly applied to the iteration process, with the total (kinetic-, specific-internal-, and magnetic-) energy density being obtained implicitly at the end of the process. An example is computed in which the convergence speed of the latter method is substantially faster than that of the former. The initializing calculation, or explicit phase, in which the electric current density, magnetic diffusion of field, energy augmentation, and zero-order approximation of the flow velocity are given, is described. Consideration is given to the iteration process, or implicit phase, from which the exact Lagrangian solution for energy density, velocity, and a magnetic field is obtained.

Wu, S. T.↗
NASA NTRS1990

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗