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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Implicit solvers for unstructured meshes

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗
NASA NTRS1991

Implicit solvers for unstructured meshes

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗
NASA NTRS2013

Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

Schwing, Alan M.↗
NASA NTRSDate not supplied

Space Needle Returns

STEP is imported into Engineering Sketch Pad. Some bodies where slightly scaled and translated in OpenCSM to create a manifold solid for the downstream meshing process. The braces at the base and columns around the core are omitted because their solids are malformed or created nonmanifold intersections. EGADS provides an initial tessellation of the surface. refine adapted the surface mesh to a curvature and feature size metric. TetGen initially filled the volume. The TetGen mesh is adapted to the Spalding Law of the Wall u+ with refine to provide the initial mesh for flow solution. Solution-based mesh adaptation is performed where FUN3D-FV computes the flow solution with the Reynolds-averaged Navier-Stokes equations coupled to the Spalart-Allmaras turbulence model. The freestream Mach number is 4 approaching 40° from the central axis of the Space Needle. The volume and surface mesh is adapted with refine to reduce estimated interpolation error in Mach number via the multiscale metric. The adapted mesh implicitly resolves the boundary layers, shocks, and expansions. The surface mesh is shown for the lee side with a slice through the volume on the left. Computational schlieren in the lower right shows density variations. A slice of the mesh is colored with Mach number in the upper right where mesh with freestream Mach number is not rendered. The volume mesh contains 64 million vertices. A NASA worm logo is sketched and extruded into a solid in OpenCSM. The worm is unioned to the Space Needle roof to produce the inset mesh image.

mesh↗
NASA NTRS1991

A fast implicit upwind solution algorithm for three-dimensional unstructured dynamic meshes

A fast implicit upwind algorithm for the solution of the time-dependent Euler equations is presented for aerodynamic analysis involving unstructured dynamic meshes. The spatial discretization of the scheme is based on the upwind approach of Roe, referred to as flux-difference splitting (FDS). The FDS approach is naturally dissipative and captures shock waves and contact discontinuities sharply. The temporal discretization of the scheme involves an implicit time-integration using a two-sweep Gauss-Seidel relaxation procedure. The procedure is computationally efficient for either steady or unsteady flow problems. A detailed description is given of the implicit upwind solution algorithm along with results which assess the capability. The results are presented for the NACA 0012 airfoil and for the Boeing 747 aircraft. The 747 geometry includes the fuselage, wing, horizontal and vertical tails, under-wing pylons, and flow-through engine nacelles. Euler solutions for the 747 aircraft on an unstructured tetrahedral mesh containing approximately 100,000 cells were obtained to engineering accuracy in less than one hour CPU time on a Cray-2 computer.

Batina, John T.↗
NASA NTRS1992

A fast implicit upwind solution algorithm for three-dimensional unstructured dynamic meshes

A fast implicit upwind algorithm for the solution of the time-dependent Euler equations is presented for aerodynamic analysis involving unstructured dynamic meshes. The spatial discretization of the scheme is based on the upwind approach of Roe, referred to as flux-difference splitting (FDS). The FDS approach is naturally dissipative and captures shock waves and contact discontinuities sharply. The temporal discretization of the scheme involves an implicit time-integration using a two-sweep Gauss-Seidel relaxation procedure. The procedure is computationally efficient for either steady or unsteady flow problems. A detailed description is given of the implicit upwind solution algorithm along with results which assess the capability. The results are presented for the NACA 0012 airfoil and for the Boeing 747 aircraft. The 747 geometry includes the fuselage, wing, horizontal and vertical tails, under-wing pylons, and flow-through engine nacelles. Euler solutions for the 747 aircraft on an unstructured tetrahedral mesh containing approximately 100,000 cells were obtained to engineering accuracy in less than one hour CPU time on a Cray-2 computer.

Batina, John T.↗
NASA NTRS1980

Calculation of two-dimensional inlet flow fields in a supersonic free stream by an implicit marching code with nonorthogonal mesh generation: User's manual

An implicit, shock-capturing finite-difference code which is used to calculate two-dimensional inlet flow fields in a supersonic free stream is explained. The Euler equations are subjected to general nonorthogonal transformation and a body-fitted coordinate system is employed. The mathematical formulation of the problem is given along with the numerical algorithm. Initial and boundary conditions, numerical stability, program limitations, and accuracy is discussed. An overall program logic as well as instructions for program use and operation are also furnished.

Biringen, S. H.↗
NASA NTRS1993

Implicit upwind solution algorithms for three-dimensional unstructured meshes

The development of implicit upwind algorithms for the solution of the three-dimensional, time-dependent Euler equations on unstructured tetrahedral meshes is described. The implicit temporal discretization involves either a two-sweep Gauss-Seide 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 a 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 NTRS1978

An implicit algorithm for the conservative transonic full potential equation using an arbitrary mesh

A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.

Holst, T. L.↗
NASA NTRS1984

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Roberts, G. O.↗
NASA NTRS1994

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Slack, David C.↗
NASA NTRSDate not supplied

Implicit Preconditioning for Explicit Multigrid Solvers on Cut-Cell Cartesian Meshes

This work assesses the effectiveness of linearized implicit Euler preconditioning for multigrid solvers using an unpreconditioned, Jacobian-free Newton Krylov method to converge the linear system of equations. Multigrid convergence rates improve to approximately 0.75 across the cases tested including a Mach 2 supersonic wedge, transonic NACA 0012 airfoil, and ONERA M6 wing. While larger Krylov subspaces increase the convergence rate, they also increase the computational cost, such that 4-8 Krylov vectors often offers the fastest turnaround. Further reductions in computational cost are achieved with a sequential hybrid preconditioner that begins with the explicit multigrid solver before transitioning to the preconditioned algorithm later on. In addition, a novel implementation of dual time stepping is extended to include both common BDF methods as well as high-order implicit Runge-Kutta schemes. This particular formulation, which uses A −1 preconditioning, is amenable to matrix-free solvers, and the L-stable methods are especially suited for meshes with arbitrarily small cut-cells. Asymptotic order of convergence is demonstrated for BDF1, BDF2, SDIRK2, and 3rd-order Radau IIA time integration with unsteady 2D vortex simulations.

ARMD↗
NASA NTRS1989

Unsteady Navier-Stokes computations over airfoils using both fixed and dynamic meshes

A finite volume implicit approximate factorization method which solves the thin layer Navier-Stokes equations was used to predict unsteady turbulent flow airfoil behavior. At a constant angle of attack of 16 deg, the NACA 0012 airfoil exhibits an unsteady periodic flow field with the lift coefficient oscillating between 0.89 and 1.60. The Strouhal number is 0.028. Results are similar at 18 deg, with a Strouhal number of 0.033. A leading edge vortex is shed periodically near maximum lift. Dynamic mesh solutions for unstalled airfoil flows show general agreement with experimental pressure coefficients. However, moment coefficients and the maximum lift value are underpredicted. The deep stall case shows some agreement with experiment for increasing angle of attack, but is only qualitatively comparable past stall and for decreasing angle of attack.

Rumsey, Christopher L.↗
NASA NTRS1988

Some numerical and physical aspects of unsteady Navier-Stokes computations over airfoils using dynamic meshes

An upwind-biased implicit approximate factorization algorithm is applied to several unsteady flows on dynamic meshes. The thin-layer form of the compressible Navier-Stokes equations is used to solve both laminar and turbulent flows over airfoils pitching about the quarter chord. Numerical aspects of the solutions are investigated, including grid and time step effects. Two methods for determining fluxes - flux-vector splitting and flux-difference splitting - are compared. Flux-difference splitting predicts results more accurately than flux-vector splitting on a coarse mesh, but both methods agree on a fine mesh. Physical aspects of the computations are also examined. An equilibrium turbulent boundary layer model computes generally better unsteady results in comparison with experiment than a nonequilibrium model for the transonic case analyzed. Also, the size and location of the primary shed vortex for an airfoil pitching up at a constant rate is calculated in good agreement with experiment for two pitch rates.

Rumsey, Christopher L.↗
NASA NTRS1992

Algebraic surface design and finite element meshes

Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.

Bajaj, Chandrajit L.↗
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 tetrahedral meshes is described. The implicit temporal discretization involves either a two-sweep Gauss-Seide 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 a 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.↗