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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

An alternating direction implicit method for the Control Data STAR-100 vector computer

An implementation of the alternating direction implicit (ADI) method for the Control Data STAR-100 computer is presented and analyzed. Two parallel algorithms, both of which are most efficient when used to solve many independent tridiagonal systems of equations, are discussed relative to their usefulness in an ADI implementation on the STAR-100 computer. It is shown that it may be desirable to alternate between the parallel algorithms as the direction of implicitness is alternated in order to eliminate the data rearrangement which would otherwise be required. The applicability of the two parallel tridiagonal solvers to several other numerical algorithms is also discussed.

Lambiotte, J. J., Jr.↗
NASA NTRS1977

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

Williams, S. D.↗
NASA NTRS1978

On implicit finite-difference simulations of three-dimensional flow

An implicit finite-difference procedure for unsteady three-dimensional flow capable of handling arbitrary geometry through the use of general coordinate transformations is described. Viscous effects are optionally incorporated with a 'thin layer' approximation of the Navier-Stokes equations. An implicit approximate factorization technique is employed so that the small grid sizes required for spatial accuracy and viscous resolution do not impose stringent stability limitations. Results obtained from the program include transonic inviscid and laminar-turbulent solutions about simple body configurations. Comparisons with existing theories and experiments are made. Numerical accuracy and the effect of three-dimensional coordinate singularities are also discussed.

Pulliam, T. H.↗
NASA NTRS1978

Supersonic flow over ablated nosetips using an unsteady, implicit numerical procedure

The axisymmetric supersonic flow over passive, that is, nonablating, indented nosetips of reentry vehicles is determined using an unsteady implicit numerical algorithm which solves either the inviscid Euler equations or the 'thin-layer' Navier-Stokes equations. A nonorthogonal independent variable transformation is used to map the distorted physical region, containing multiple zones of embedded subsonic flow into a rectangular computational domain at whose boundaries the required permeable or impermeable boundary conditions are simulated. Use of the implicit algorithm results in faster convergence to the steady state because of a larger allowable time step over conventional explicit schemes. The numerical results obtained compare favorably with existing experimental data for very mildly and severely indented blunt nosetips.

Kutler, P.↗
NASA NTRS1979

Alternating direction implicit methods for parabolic equations with a mixed derivative

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.

Beam, R. M.↗
NASA NTRS1979

An implicit factored scheme for the compressible Navier-Stokes equations. II - The numerical ODE connection

An attempt is made to establish a connection between linear multistep methods for applications to ordinary differential equations and their extension (by approximate factorization) to alternating direction implicit methods for partial differential equations. An earlier implicit factored scheme for the compressible Navier-Stokes equations is generalized by innovations that (1) increase the class of temporal difference schemes to include all linear multistep methods, (2) optimize the class of unconditionally stable factored schemes by a new choice of unknown variable, and (3) improve the computational efficiency by the introduction of quasi-one-leg methods.

Beam, R. M.↗
NASA NTRS1980

Supersonic flow over three-dimensional ablated nosetips using an unsteady implicit numerical procedure

The three-dimensional supersonic flow over passive, that is, nonablating, indented nosetips of reentry vehicles is determined using an unsteady implicit numerical algorithm which solves either the inviscid Euler equations or the 'thin-layer' Navier-Stokes equations. A nonorthogonal independent variable transformation is used to map the distorted physical domain, containing multiple zones of embedded subsonic flow and separated flow regions into a rectangular computational volume at whose boundaries the required permeable or impermeable boundary conditions are simulated. Use of the implicit algorithm results in faster convergence to the steady state because of a larger allowable time step over conventional explicit schemes. The numerical results obtained compare favorably with existing numerical solutions and experimental data for simple spheres which validates the program. Results are also presented for analytically defined indented bodies for both laminar and turbulent flow conditions that demonstrate the program's capability for computing such flows.

Kutler, P.↗
NASA NTRS1979

A fast semi-implicit algorithm for problems of mixed type

Certain physical processes are modeled by partial differential equations which are parabolic over part of the domain and elliptic over the remainder. A family of semi-implicit algorithms which are well suited to initial-boundary value problems of this mixed type is discussed. One important feature of these algorithms is the use of an approximate inverse for the solution of the implicit linear system. A strong error analysis results in an estimate of the total error as a function of approximate inverse error e and time step h.

Frederickson, P. O.↗
NASA NTRS1978

On the construction and application of implicit factored schemes for conservation laws

Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

Warming, R. F.↗
NASA NTRS1980

Alternating direction implicit methods for parabolic equations with a mixed derivative

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A(0)-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A(0)-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

Beam, R. M.↗
NASA NTRS1981

Implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows

A fully implicit set of boundary conditions is developed for the solution of the parabolized Navier-Stokes equations for supersonic flow in two dimensions. Shock fitting is employed at the shock and the body has no-slip and specified temperature conditions. A specified heat transfer condition at the wall can be handled in a similar manner. In addition, the shock location is advanced in space in a fully implicit manner by utilizing the Rankine-Hugoniot conditions along with global conservation of mass.

Barnett, M.↗
NASA NTRS1981

Implicit calculations of transonic flows using monotone methods

Implicit approximate-factorization algorithms have been developed that use monotone methods for the calculation of steady and unsteady transonic flows governed by the small-disturbance-potential equation. These algorithms use the new Engquist-Osher switch in the type-dependent differencing in place of the standard Murman-Cole switch. The resulting algorithms are more stable; hence, calculations can be done more efficiently. For steady flows, the convergence rate is about 35% faster, and for unsteady flows the allowable time step is about 10 times larger. These improvements are achieved with no increase in computer storage and with only minor modifications in codes that use the Murman-Cole switch. Also an implicit algorithm has been developed for the steady full-potential equation in one-dimension, which uses monotone methods.

Goorjian, P. M.↗
NASA NTRS1980

The solution of variable-step implicit difference equations for dynamic systems analysis

A semi-implicit iterative technique is given for the solution of implicit matrix difference equations which arise in variable-step direct time integration of dynamic systems equations. For all practical purposes, the technique avoids repeated refactoring of the stepsize-dependent solution matrix and achieves the solution convergence for engineering accuracy requirements within a permissible number of iterations. Extension of the present method to nonlinear problems treated by the pseudo-force procedure is straightforward. For nonlinear solution procedures based on the tangent modulus formulation, the technique requires modification to make use of the tangent stiffness matrix. It is noted that the question of whether to include the nonlinear terms within the iteration loop has not yet been resolved.

Park, K. C.↗
NASA NTRS1982

Semi-implicit transient analysis procedures for structural dynamics analysis

A semi-implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix. The procedure, if properly implemented, requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures. Guidelines for splitting the stiffness matrix into upper and lower matrices are established, which among other things are designed to satisfy a correct transmission of rigid-body motions from element (or grid) to its adjacent elements.

Park, K. C.↗
NASA NTRS1983

New implicit boundary procedures - Theory and applications

Analytical techniques for the application of implicit boundary conditions for inviscid flows to shock and body boundary layer conditions involving the Euler equations are presented. The theory of characteristics is used to update boundary points with spatial second order accuracy. The method is useful for implicit schemes which feature approximate factorization, and as such is incorporated into an existing PNS code. Examples are provided in terms of flows over a cone, over a maneuverable reentry vehicle, and over a finned vehicle. Improvements in the convergence rate are demonstrated for the conical flow solutions.

Rai, M. M.↗
NASA NTRS1983

An enhanced version of an implicit code for the Euler equations

A two-dimensional implicit finite-difference code is applied to the inviscid Euler equations to compute transonic flow past airfoils in order to provide well-documented standard test cases for the general user community. The code is an improved version of Steger's 1976 implicit code. Enhancements include the use of up-wind differencing in supersonic regions before shocks and a variable time step to accelerate convergence. An airfoil grid generation routine based on algebraic techniques is employed. The grids are clustered near shocks to improve resolution. Computed results are compared with other numerical results from the literature.

Pulliam, T. H.↗
NASA NTRS1983

Application of the implicit MacCormack scheme to the PNS equations

The two-dimensional parabolized Navier-Stokes equations are solved using MacCormack's (1981) implicit finite-difference scheme. It is shown that this method for solving the parabolized Navier-Stokes equations does not require the inversion of block tridiagonal systems of algebraic equations and allows the original explicit scheme to be employed in those regions where implicit treatment is not needed. The finite-difference algorithm is discussed and the computational results for two laminar test cases are presented. Results obtained using this method for the case of a flat plate boundary layer are compared with those obtained using the conventional Beam-Warming scheme, as well as those obtained from a boundary layer code. The computed results for a more severe test of the method, the hypersonic flow past a 15 deg compression corner, are found to compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

Lawrence, S. L.↗
NASA NTRS1983

Implicit conservative characteristic modeling schemes for the Euler equations - A new approach

An implicit characteristic-modeling solution scheme for the Euler equations is presented. The scheme does not require the governing equations to be written in characteristic variables or the flux terms to be split into positive and negative contributions. For the two-dimensional problem of a shock wave reflecting from a flat plate, this feature and the simple solution algorithm combine to reduce the computational work per mesh point by 40 percent from that required by a standard, central-difference, implicit, solution algorithm. Application of the method to the quasi-one-dimensional nozzle flow equations for subsonic and supersonic flows without shocks shows the method to be well-conditioned for large time steps.

Wornom, S. F.↗