Linking solver characteristics, solving processes and solution attributes: A data explainer for an open innovation generated robotic design dataset
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Zoe Szajnfarber↗
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Results for “solver”
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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High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes
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D.Z. Huang↗
A study of the efficiency of various Navier-Stokes solvers
A comparative study of the efficiency of some finite difference methods for the solution of the Navier-Stokes equations was conducted. The study was restricted to the two-dimensional steady, uniform property vorticity-stream function equations. The comparisons were drawn by recording the CPU time required to obtain a solution as well as the accuracy of this solution using five numerical methods: central differences, first order upwind differences, second order upwind differences, exponential differences, and an ADI solution of the central difference equations. Solutions were obtained for two test cases: a recirculating eddy inside a square cavity with a moving top, and an impinging jet flow. The results show that whenever the central difference method is stable it generates results with a given accuracy for less CPU time than any other method.
Atias, M.↗
NASA-Ames three-dimensional potential flow analysis system (POTFAN) equation solver code (SOLN) version 1
A computer program known as SOLN was developed as an independent segment of the NASA-Ames three-dimensional potential flow analysis systems of linear algebraic equations. Methods used include: LU decomposition, Householder's method, a partitioning scheme, and a block successive relaxation method. Due to the independent modular nature of the program, it may be used by itself and not necessarily in conjunction with other segments of the POTFAN system.
Davis, J. E.↗
A rapid solver for hyperbolic systems of equations
A numerical method is proposed for solving the time-dependent compressible Navier-Stokes equations in two dimensions. The equations are time-split into a hyperbolic part and a parabolic part. This paper describes an explicit numerical method for solving the hyperbolic (inviscid) part. The hyperbolic operator is explicit, conservative, uses characteristic relations to predict convection and pressure fields, and is stable under a specified condition.
Maccormack, R. W.↗
A modular minicomputer based Navier-Stokes solver
The basic module consists of a minicomputer, low cost peripheral storage device (disk) and a modest number (8-12) of microcomputer modules. A simple arrangement, where the microcomputers are connected to a single time multiplexed bus, only communicating to the host minicomputer, will be efficient. By running the machine in a dedicated mode for long periods of time, it will be possible to obtain a large number of solutions. As such, the device should be useful as a research tool. A scheme is outlined to assemble a number of these computing modules in parallel to decrease computing time. The advantages and disadvantages are discussed of using a number of these systems assembled in a loosely coupled configuration, each independently computing a separate flow, to give a very high throughput.
Steinhoff, J.↗
A Navier-Stokes fast solver for turbulence modeling applications
A computer code for the evaluation and/or optimization of the predicative potential of second order turbulent closure models in simple two dimensional flow configurations is discussed. A procedure for the numerical solution of the steady constant property Navier-Stokes equations are described together with algebraic, one dimensional and two dimensional equations of turbulence closure models. Four turbulence models are compared with several sets of experimental data. The effects of initial conditions and boundary conditions are also described. The effects of purely numerical parameters, such as mesh size, boundary locations, and convergence criteria are presented.
Murphy, J. D.↗
A PANSONIC Navier-Stokes solver
A finite-difference formulation of the full Navier-Stokes equations which demonstrates a capability to economically solve two-dimensional problems has been developed. The basic algorithm was derived from the full, Reynolds-averaged, conservative, Navier-Stokes equations expressed in curvilinear coordinates. Eddy viscosity was determined by the Baldwin and Lomax algebraic turbulence model. This non-iterative, second-order accurate, implicit, numerical algorithm is based on the approximate factorization finite-difference scheme of Beam and Warming. Results indicate a facility for solving subsonic, transonic, and supersonic (hence PANSONIC) flows about arbitrary airfoils for a wide range of Reynolds numbers, Mach numbers, and angles of attack. Current computations demonstrate that vectorized implementations of this algorithm can solve steady-state, two-dimensional problems in five to ten minutes of computer time.
Cooper, G. K.↗
Approximate factorization with an elliptic pressure solver for incompressible flow
Two-dimensional curvilinear coordinates are used to solve the incompressible Navier-Stokes equations, in conjunction with approximate factorization for the solution of the momentum equation and the successive overrelaxation by lines method for the solution of a Poisson equation for the pressure. The combined algorithm, although not fully explicit, is marginally stable at Reynolds numbers lower than 10,000 and time increments of 0.01. Pressure distributions calculated for attack angles of zero and 6 deg are of the same shape as the experimental curves, but are shifted to one side.
Bernard, R. S.↗
Fast Euler solver for steady, 1-dimensional flows
A numerical technique to solve the Euler equations for steady, one dimensional flows is presented. The technique is essentially implicit, but is structured as a sequence of explicit solutions for each Riemann variable separately. Each solution is obtained by integrating in the direction prescribed by the propagation of the Riemann variables. The technique is second-order accurate. It requires very few steps for convergence, and each step requires a minimal number of operations. Therefore, it is three orders of magnitude more efficient than a standard time-dependent technique. The technique works very well for transonic flows and provides shock fitting with errors as small as 0.001. Results are presented for subsonic problems. Errors are evaluated by comparison with exact solutions.
Moretti, G.↗
Algorithms and data structures for adaptive multigrid elliptic solvers
Adaptive refinement and the complicated data structures required to support it are discussed. These data structures must be carefully tuned, especially in three dimensions where the time and storage requirements of algorithms are crucial. Another major issue is grid generation. The options available seem to be curvilinear fitted grids, constructed on iterative graphics systems, and unfitted Cartesian grids, which can be constructed automatically. On several grounds, including storage requirements, the second option seems preferrable for the well behaved scalar elliptic problems considered here. A variety of techniques for treatment of boundary conditions on such grids are reviewed. A new approach, which may overcome some of the difficulties encountered with previous approaches, is also presented.
Vanrosendale, J.↗
A fast Euler solver for steady flows
A numerical technique to solve the Euler equations for steady, two-dimensional flows is presented. The technique extends to two-dimensional problems a formulation which was found to be extremely efficient for one-dimensional flows. Generalized Riemann variables are defined along two families of orthogonal coordinates, and integrated separately, sweeping back and forth alternatively along coordinate lines. The technique is second-order accurate and converges very rapidly. In addition, each step requires a minimal number of operations. Preliminary results for subsonic and transonic shockless flows are presented and discussed.
Moretti, G.↗
Vectorized multigrid Poisson solver for the CDC CYBER 205
The full multigrid (FMG) method is applied to the two dimensional Poisson equation with Dirichlet boundary conditions. This has been chosen as a relatively simple test case for examining the efficiency of fully vectorizing of the multigrid method. Data structure and programming considerations and techniques are discussed, accompanied by performance details.
Barkai, D.↗
An explicit predictor-corrector solver with applications to Burgers' equation
Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.
Dey, S. K.↗
An incompressible Navier-Stokes flow solver in three-dimensional curvilinear coordinate systems using primitive variables
An implicit, finite-difference computer code has been developed to solve the incompressible Navier-Stokes equations in a three-dimensional, curvilinear coordinate system. The pressure-field solution is based on the pseudo compressibility approach in which the time derivative pressure term is introduced into the mass conservation equation to form a set of hyperbolic equations. The solution procedure employs an implicit, approximate factorization scheme. The Reynolds stresses, that are uncoupled from the implicit scheme, are lagged by one time-step to facilitate implementing various levels of the turbulence model. Test problems for external and internal flows are computed, and the results are compared with existing experimental data. The application of this technique for general three-dimensional problems is then demonstrated.
Kwak, D.↗
Second order closure for the calculation of compressible wall bounded flows with an implicit Navier-Stokes solver
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Vandromme, D.↗
Progress in development of a Navier-Stokes solver for evaluation of iced airfoil performance
A method is being developed for evaluation of the flow field behavior about an airfoil with significant ice accretion on the leading edge. The computer code, being evaluated for this purpose, solves the Navier-Stokes equations in a body-fitted curvilinear coordinate system. This requires the use of a grid generation code to transform the x-y coordinates of the physical space into xi-eta coordinates of the computational space. Evaluation of the suitability of these two codes for predicting iced airfoil performance is presently being carried out in anticipation of use in an overall icing analysis effort. Results of this evaluation to date indicate good correlation with known information on clean airfoils. Preliminary results for rime and glaze, iced airfoil shapes are also presented.
Potapczuk, M. G.↗
Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method
An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.
Chang, S. C.↗