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Cooke, C. H.

Publications and source records attributed to Cooke, C. H..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

Cooke, C. H.↗
NASA NTRS1983

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow has been developed. The revision incorporates balancing of massflow rates on each marching step in order to maintain front-to-back continuity during the calculation. Qualitative agreement with analytical predictions and experimental results has been obtained for some flows with well-known solutions.

Cooke, C. H.↗
NASA NTRS1981

A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

Cooke, C. H.↗
NASA NTRS1981

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

Cooke, C. H.↗
NASA NTRS1981

A simplified model for the viscous crossflow in a slotted test section

A simplified physical model is constructed which simulates the viscous crossflow in a fluid layer near the slots at a fixed streamwise location in a slotted wind tunnel. For low to moderate Reynolds numbers, numerical solutions of the two-dimensional, incompressible Navier-Stokes equations in stream function and vorticity, which govern the model flow, are obtained. Fairly general slot geometry is incorporated by means of the Thompson-Thames-Mastin transformation. An approximate factorization scheme with cyclic acceleration parameters is employed to solve a finite difference analog of the stream function equation. The vorticity equation is numerically solved with a modified version of the classical alternating direction implicit (ADI) scheme. Although no quantitative assessment of solution accuracy can be made, numerical results for variations in incremental wall pressure around the slot are at least qualitatively similar to some experimental results of Berndt and Sorenson.

Cooke, C. H.↗
NASA NTRS1979

A simplified model for the viscous crossflow in a slotted test section

A simplified physical model was constructed which simulates the viscous crossflow in a fluid layer near the slots at a fixed streamwise location in a slotted wind tunnel. For low to moderate Reynolds numbers, numerical solutions of the two dimensional, incompressible Navier-Stokes equations in stream function and vorticity, which govern the model flow, were obtained. Fairly general slot geometry was incorporated by means of the Thompson-Thames-Mastin transformation. An approximate factorization scheme with cyclic acceleration parameters was employed to solve a finite difference analog of the stream function equation. The vorticity equation was numerically solved with a modified version of the classical alternating direction implicit scheme. Although no quantitative assessment of solution accuracy can be made, numerical results for variations in incremental wall pressure around the slat are at least qualitatively similar to some experimental results.

Cooke, C. H.↗
NASA NTRS1979

A shock capturing application of the finite element method

The paper is concerned with the development of finite element algorithms for the solution of viscous compressible flow problems with possible embedded shocks and recirculation regions. As a first step, the calculation in Cartesian coordinates of uniform flow on a rectangular region which encounters an embedded oblique shock with known turning angle is considered. A code is developed which is then used for computation of the boattail plume simulator problem in cylindrical coordinates. Oblique shock calculations are performed and the results are compared with a known finite difference solution.

Cooke, C. H.↗
NASA NTRS1979

A two dimensional model of viscous slot flow

The effects of viscosity on flows through slots are investigated. Using Briley's formulation of the Alternating Direction Implicit method together with the Thompson transformation, numerical solution of viscous incompressible flow through a slot is simulated, for Reynolds number 1000 and openness ratio one tenth. The problem is formulated in terms of stream function and vorticity. A wall iteration of Israeli type is employed to iteratively induce the no slip condition on velocity.

Cooke, C. H.↗
NASA NTRS1978

A split band-Cholesky equation solving strategy for finite element analysis of transient field problems

The paper describes the split-Cholesky strategy for banded matrices arising from the large systems of equations in certain fluid mechanics problems. The basic idea is that for a banded matrix the computation can be carried out in pieces, with only a small portion of the matrix residing in core. Mesh considerations are discussed by demonstrating the manner in which the assembly of finite element equations proceeds for linear trial functions on a triangular mesh. The FORTRAN code which implements the out-of-core decomposition strategy for banded symmetric positive definite matrices (mass matrices) of a coupled initial value problem is given.

Cooke, C. H.↗
NASA NTRS1977

A block iterative LU solver for weakly coupled linear systems

A hybrid technique, called the block iterative LU solver, is proposed for solving the linear equations resulting from a finite element numerical analysis of certain fluid dynamics problems where the equations are weakly coupled between distinct sets of variables. Either the block Jacobi iterative method or the block Gauss-Seidel iterative solver is combined with LU decomposition.

Cooke, C. H.↗
NASA NTRS1977

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The continuous cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗
NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗
NASA NTRS1975

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Cooke, C. H.↗
NASA NTRS1975

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Rudy, D. H.↗
NASA NTRS1975

STICAP: A linear circuit analysis program with stiff systems capability. Volume 1: Theory manual

STICAP (Stiff Circuit Analysis Program) is a FORTRAN 4 computer program written for the CDC-6400-6600 computer series and SCOPE 3.0 operating system. It provides the circuit analyst a tool for automatically computing the transient responses and frequency responses of large linear time invariant networks, both stiff and nonstiff (algorithms and numerical integration techniques are described). The circuit description and user's program input language is engineer-oriented, making simple the task of using the program. Engineering theories underlying STICAP are examined. A user's manual is included which explains user interaction with the program and gives results of typical circuit design applications. Also, the program structure from a systems programmer's viewpoint is depicted and flow charts and other software documentation are given.

Cooke, C. H.↗
NASA NTRS1972

On stiffly stable implicit linear multistep methods.

The motivation to increase the step size with no degradation of numerical accuracy and stability has led to the discovery of particular members of the class of stiffly stable implicit linear multistep algorithms. Sufficient conditions for a consistent linear multistep method to be stiffly stable are given. These conditions involve properties of the stability mapping from the extended complex plane onto itself.

Cooke, C. H.↗