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Hirsh, R. S.

Publications and source records attributed to Hirsh, R. S..

7 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Numerical solution of supersonic three-dimensional free-mixing flows using the parabolic-elliptic Navier-Stokes equations

A numerical method is presented for solving the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to three-dimensional supersonic laminar jet flow issuing parallel with a supersonic free stream. A coordinate transformation is introduced which maps the boundaries at infinity into a finite computational domain in order to eliminate difficulties associated with the imposition of free-stream boundary conditions. Results are presented for an approximate circular jet, a square jet, varying aspect ratio rectangular jets, and interacting square jets. The solution behavior varies from axisymmetric to nearly two-dimensional in character. For cases where comparisons of the present results with those obtained from shear layer calculations could be made, agreement was good.

Hirsh, R. S.↗
NASA NTRS1976

Comments on the role of diagonal dominance in implicit difference methods

Numerical tests were made for a model of the Navier-Stokes equations using a second-order accurate implicit scheme which guarantees diagonal dominance. The results suggest that the failure of implicit methods using large marching steps may not always be attributed to the lack of diagonal dominance in the coefficient matrix. In some cases the failure may be caused by a nonlinear instability associated with the solution method.

Rudy, D. H.↗
NASA NTRS1975

Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique

A general fourth order differencing scheme is developed and applied to three viscous test problems to verify the accuracy and applicability of the technique. The procedure is atypical since only three nodes are necessary to obtain the desired fourth order accuracy. This is accomplished by a differencing technique which considers the function and all necessary derivatives as unknowns. The relations for these derivatives yield simple tridiagonal equations which can be easily solved. Comparisons of the fourth order results with those computed using second order methods are presented for the test problems and clearly indicate that the accuracy achieved by these fourth order computations is always significantly better than current second order procedures.

Hirsh, R. S.↗
NASA NTRS1975

Calculation of supersonic three-dimensional free-mixing flows using the parabolic-elliptic Navier-Stokes equations

A numerical method is presented which is valid for integration of the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to the three-dimensional supersonic flow of a jet issuing into a supersonic free stream. Difficulties associated with the imposition of free-stream boundary conditions are noted, and a coordinate transformation, which maps the point at infinity onto a finite value, is introduced to alleviate these difficulties. Results are presented for calculations of a square jet and varying-aspect-ratio rectangular jets. The solution behavior varies from axisymmetry for the square jet to nearly two-dimensional for the high-aspect-ratio rectangle, although the computation always calculates the flow as though it were truly three-dimensional.

Hirsh, R. S.↗
NASA NTRS1975

Second-order non-iterative ADI solution of non-linear partial differential equations

A new method for the solution of non-linear partial differential equations by an ADI procedure is described. Although the method is second order accurate in time, it does not require either iterations or predictor corrector methods to overcome the nonlinearity of the equations. Thus the computational effort required for the solution of the non-linear problem becomes similar to that required for the linear case. The method is applied to a two-dimensional 'extended Burgers equation'. Linear stability is studied, and some numerical solutions obtained. The improved accuracy obtained by the 2nd order truncation error is clearly manifested.

Wolfshtein, M.↗