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At least 109 records · Page 6
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NASA NTRS2014

Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers

This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.

Schwing, Alan M.↗
NASA NTRS1988

Computations of vortical supersonic flows over a blunt-nose-cylinder at high angles of attack

Three-dimensional, viscous, and separated flows over a blunt-nose-cylinder at 20, 32, and 44-deg attack angles were computed. The approaching freestream was at a Mach number of 1.6 and a unit Reynolds number of 2 x 10 to the 6th/ft with a total temperature of 585 R. The cylinder used for the computations had a length-to-diameter ratio of 6.67 with a base diameter of 3 in. The flowfield was dominated by large-scale and multiple vortices generated by crossflow separation. The effect of turbulence on the flow structure of one case was modeled algebraically with modifications to correct the length and velocity scales in the regions of separation. The mass averaged Navier-Stokes equations were solved by an approximately factored, upwind-biased, implicit, finite volume scheme. The initialization of the flows was enhanced by a mesh sequencing strategy applied to the diagonalized form of the discretized equations. The convergence to steady-state was accelerated by a multigrid algorithm and using the block inversions for the discretized equations. Calculations were compared with experimental results.

Baysal, O.↗
NASA NTRS1992

Finite-element solution scheme for compressible viscous flow

Adaptivity offers the possibility of using FEM for problems that are otherwise intractable. The solution algorithm is combined with an adaptive approach in which the unstructured portion of the grid is adaptively regenerated as the solution proceeds; the structured portion of the mesh is modified accordingly, to ensure both compatibility along the interface between the implicit and explicit element groups and increased resolution of the viscous layer. The approach offers significant computational savings in 3D simulations.

Hassan, O.↗
NASA NTRS1989

Low gravity transfer line chilldown

A code has been developed that solves for the transfer line chilldown time and flow and heat transfer characteristics in one-g environment. The code solves the transient, one dimensional, space averaged mass, momentum, and energy conservation equations for liquid-vapor two-phase flow in tubes. The physical configuration solved is that appropriate for bottom coolant injection in a vertically supported heated tube. Four distinct regions are considered consecutively: fully liquid, inverted annular, dispersed, and fully vapor flow. The conservation equations for both the liquid and the vapor are solved in each region separately. Also, in each region the mass and energy transport between each phase as well as the energy and momentum transport between the tube wall and the fluid are accounted for. A finite wall thickness is also considered. The model described above was solved numerically through a mixed finite difference scheme with forward time marching. The inverted annular regime was resolved using a semi-implicit finite differencing while the dispersed regime was solved explicitly. Also, a staggered mesh was used in which the velocity was resolved at mesh boundaries while all other field variables were resolved at the mesh centroids. Different mesh sizes were used depending on the region of solution. A coarse mesh was used in the dispersed flow region while a much finer mesh was used in both the inverted annular flow region and the tube walls.

B. N. Antar↗
NASA NTRS1987

Composite grid and finite-volume LU implicit scheme for turbine flow analysis

A composite grid was generated in an attempt to improve grid quality for a typical turbine blade with large camber in terms of mesh control, smoothness, and orthogonality. This composite grid consists of the C grid (or O grid) in the immediate vicinity of the blade and the H grid in the upstream region and in the middle of the blade passage between the C grids. It provides a good boundary layer resolution around the leading edge region for viscous calculation, has orthogonality at the blade surface and slope continuity at the C-H (or O-H) interface, and has flexibility in controlling the mesh distribution in the upstream region without using excessive grid points. This composite grid eliminates the undesirable qualities of a single grid when generated for a typical turbine geometry. A finite-volume lower-upper (LU) implicit scheme can be used in solving for the turbine flows on the composite grid. This grid has a special grid node that is connected to more than four neighboring nodes in two dimensions and to more than six nodes in three dimensions. But the finite-volume approach poses no problem at the special point because each interior cell has only four neighboring cells in two dimensions and only six cells in three dimensions. The finite-volume LU implicit scheme was demonstrated to be robust and efficient for both external and internal flows in a broad flow regime.

Choo, Yung K.↗
NASA NTRS1987

Composite grid and finite-volume LU implicit scheme for turbine flow analysis

A composite grid was generated in an attempt to improve grid quality for a typical turbine blade with large camber in terms of mesh control, smoothness, and orthogonality. This composite grid consists of the C grid (or O grid) in the immediate vicinity of the blade and the H grid in the upstream region and in the middle of the blade passage between the C grids. It provides a good boundary layer resolution around the leading edge region for viscous calculation, has orthogonality at the blade surface and slope continuity at the C-H (or O-H) interface, and has flexibility in controlling the mesh distribution in the upstream region without using excessive grid points. This composite grid eliminates the undesirable qualities of a single grid when generated for a typical turbine geometry. A finite-volume lower-upper (LU) implicit schemes can be used in solving for the turbine flows on the composite grid. This grid has a special grid node that is connected to more than four neighboring nodes in two dimensions and to more than six nodes in three dimensions. But the finite-volume approach poses no problem at the special point because each interior cell has only four neighboring cells in two dimensions and only six cells in three dimensions. The finite-volume LU implicit scheme was demonstrated to be robust and efficient for both external and internal flows in a broad flow regime.

Choo, Yung K.↗
NASA NTRS1989

An efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations

A cell-vertex scheme for the three-dimensional Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing with locally varying coefficients, a multigrid method and carefully controlled dissipative terms, very good convergence rates are obtained for two- and three-dimensional flows. Details of the acceleration techniques, which are important for convergence on meshes with high aspect-ratio cells, are discussed. Emphasis is put on the analysis of the stability properties of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios.

Radespiel, R.↗
NASA NTRS1999

Implicit Space-Time Conservation Element and Solution Element Schemes

Artificial numerical dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The new schemes presented are two highly accurate implicit solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the schemes are analysed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Chang, Sin-Chung↗
NASA NTRS1982

Laminar flow transition: A large-eddy simulation approach

A vectorized, semi-implicit code was developed for the solution of the time-dependent, three dimensional equations of motion in plane Poiseuille flow by the large-eddy simulation technique. The code is tested by comparing results with those obtained from the solutions of the Orr-Sommerfeld equation. Comparisons indicate that finite-differences employed along the cross-stream direction act as an implicit filter. This removes the necessity of explicit filtering along this direction (where a nonhomogeneous mesh is used) for the simulation of laminar flow transition into turbulence in which small scale turbulence will be accounted for by a subgrid scale turbulence model.

Biringen, S.↗
NASA NTRS1989

A Navier-Stokes solver for high speed equilibrium flows and application to blunt bodies

This paper presents a finite element method for the solution of Navier-Stokes equations with the assumption of thermodynamic and chemical equilibrium. The method employs an upwind finite element technique with an implicit time-marching scheme for the solution, and uses an adaptively generated unstructured triangular mesh with several layers of quadrilateral elements near solid walls. The complexity associated with the assumption that the flow is in equilibrium is treated consistently, and the inviscid flux Jacobian matrices are derived. Several problems involving inviscid and viscous hypersonic flow past blunt are solved. Results are compared with other numerical results and experimental data, and generally good agreement is observed.

Prabhu, Ramadas K.↗
NASA NTRS1992

An implicit multigrid scheme for hypersonic strong-interaction flowfields

An implicit multigrid method for the compressible Navier-Stokes equations is applied to a series of two-dimensional, steady, laminar hypersonic flows over a compression ramp, including both attached and separated flow conditions. The algorithm uses upwind-biased differencing for the convective and pressure terms and central differencing for the shear-stress and heat-transfer terms. An implicit spatially factored scheme is used to advance the solution in terms on a given mesh, and a V-cycle multigrid strategy is used to accelerate convergence. The multigrid algorithm provided an order of magnitude decrease in the computational time required to obtain a converged position of the separation location and enabled a substantially grid-independent result to be obtained for each of the flows considered.

Thomas, James L.↗
NASA NTRS1985

Recent improvements in efficiency, accuracy, and convergence for implicit approximate factorization algorithms

In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.

Pulliam, T. H.↗
NASA NTRS1987

A combined Eulerian-Lagrangian analysis for computation of two-phase flows

A combined Eulerian-Lagrangian analysis, which combines a linearized block implicit Navier-Stokes analysis for the continuous phase with a Lagrangian analysis for the motion of the droplet phase to simulate evaporating two-phase flows, has been developed. A unique aspect of this analysis is that the Lagrangian equations for the droplet motion have been transformed into the Eulerian computational space using coordinate transformation resulting in better computational efficiency. Use of the present implicit procedure for the continuous phase makes it possible to efficiently use a locally highly refined mesh. The coupling of the continuous phase and the droplet phase analyses is such that it allows the use of convergence acceleration techniques for steady-state problems, as well as making it possible to simulate transient flows. A rapidly evaporating two-phase flow caused by spray of liquid nitrogen in gaseous nitrogen has been used as a test problem to demonstrate the computer code using this analysis.

Sabnis, J. S.↗
NASA NTRS1986

Aerodynamics of Engine-Airframe Interaction

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

Caughey, D. A.↗
NASA NTRS2002

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

The rapid increase in available computational power over the last decade has enabled higher resolution flow simulations and more widespread use of unstructured grid methods for complex geometries. While much of this effort has been focused on steady-state calculations in the aerodynamics community, the need to accurately predict off-design conditions, which may involve substantial amounts of flow separation, points to the need to efficiently simulate unsteady flow fields. Accurate unsteady flow simulations can easily require several orders of magnitude more computational effort than a corresponding steady-state simulation. For this reason, techniques for improving the efficiency of unsteady flow simulations are required in order to make such calculations feasible in the foreseeable future. The purpose of this work is to investigate possible reductions in computer time due to the choice of an efficient time-integration scheme from a series of schemes differing in the order of time-accuracy, and by the use of more efficient techniques to solve the nonlinear equations which arise while using implicit time-integration schemes. This investigation is carried out in the context of a two-dimensional unstructured mesh laminar Navier-Stokes solver.

Jothiprasad, Giridhar↗
NASA NTRS1996

Implicit Extrapolation Methods for Variable Coefficient Problems

Implicit extrapolation methods for the solution of partial differential equations are based on applying the extrapolation principle indirectly. Multigrid tau-extrapolation is a special case of this idea. In the context of multilevel finite element methods, an algorithm of this type can be used to raise the approximation order, even when the meshes are nonuniform or locally refined. Here previous results are generalized to the variable coefficient case and thus become applicable for nonlinear problems. The implicit extrapolation multigrid algorithm converges to the solution of a higher order finite element system. This is obtained without explicitly constructing higher order stiffness matrices but by applying extrapolation in a natural form within the algorithm. The algorithm requires only a small change of a basic low order multigrid method.

Jung, M.↗
NASA NTRS2003

Development of a Dynamically Configurable, Object-Oriented Framework for Distributed, Multi-modal Computational Aerospace Systems Simulation: Second Year Progress Report

Mesh generation has long been recognized as a bottleneck in the CFD process. While much research on automating the volume mesh generation process have been relatively successful,these methods rely on appropriate initial surface triangulation to work properly. Surface discretization has been one of the least automated steps in computational simulation due to its dependence on implicitly defined CAD surfaces and curves. Differences in CAD peometry engines manifest themselves in discrepancies in their interpretation of the same entities. This lack of "good" geometry causes significant problems for mesh generators, requiring users to "repair" the CAD geometry before mesh generation. The problem is exacerbated when CAD geometry is translated to other forms (e.g., IGES )which do not include important topological and construction information in addition to entity geometry. One technique to avoid these problems is to access the CAD geometry directly from the mesh generating software, rather than through files. By accessing the geometry model (not a discretized version) in its native environment, t h s a proach avoids translation to a format which can deplete the model of topological information. Our approach to enable models developed in the Denali software environment to directly access CAD geometry and functions is through an Application Programming Interface (API) known as CAPRI. CAPRI provides a layer of indirection through which CAD-specific data may be accessed by an application program using CAD-system neutral C and FORTRAN language function calls. CAPRI supports a general set of CAD operations such as truth testing, geometry construction and entity queries.

Afjeh, Abdollah A.↗
NASA NTRS1994

An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids

An implicit, Navier-Stokes solution algorithm is presented for the computation of turbulent flow on unstructured grids. The inviscid fluxes are computed using an upwind algorithm and the solution is advanced in time using a backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with a point-implicit relaxation scheme. This methodology provides a viable and robust algorithm for computing turbulent flows on unstructured meshes. Results are shown for subsonic flow over a NACA 0012 airfoil and for transonic flow over a RAE 2822 airfoil exhibiting a strong upper-surface shock. In addition, results are shown for 3 element and 4 element airfoil configurations. For the calculations, two one equation turbulence models are utilized. For the NACA 0012 airfoil, a pressure distribution and force data are compared with other computational results as well as with experiment. Comparisons of computed pressure distributions and velocity profiles with experimental data are shown for the RAE airfoil and for the 3 element configuration. For the 4 element case, comparisons of surface pressure distributions with experiment are made. In general, the agreement between the computations and the experiment is good.

Anerson, W. Kyle↗