Multidimensional time dependent method of characteristics. (English) Zbl 0638.76085
Summary: A numerical technique based on the theory of characteristics in multidimensional gasdynamics is developed. The characteristic equations are recast into a form in which linear combinations of the gasdynamic variables are integrated along initially characteristic rays, and the solution is subsequently obtained by the inersion of a system of linear algebraic equations. This formulation facilitates the imposition of boundary conditions, which are usually algebraic, and can therefore be directly incorporated into the linear system. The choice of boudary treatments, which is guided by the theory of characteristics, is described in detail. The method was successfully applied to sample problems in two- and three-dimensional nozzle flow. While familiar, these examples involve a variety of boundary conditions.
Keywords:
theory of characteristics; multidimensional gasdynamics; initially characteristic rays; linear algebraic equations; boundary conditions; three-dimensional nozzle flowReferences:
| [1] | Ransom, V. H.; Hoffman, J. D.; Thompson, H. D., A second-order bicharacteristics method for three-dimensional study supersonic flow, AIAA J., 10, 1573 (1972) · Zbl 0261.76045 |
| [2] | Butler, D. S., The numerical solution of hyberbolic systems of partial differential equations in three independent variables, (Proc. R. Soc., 255A (1960)), 232 · Zbl 0099.41501 |
| [3] | Martinon, J., Use of the characteristic method for the prediction of the three-dimensional flow field in high transonic compressors, Trans. ASME, 102, 96 (1980) |
| [4] | Marcum, D. L.; Hoffman, J. D., Calculation of three-dimensional flowfields by the unsteady method of characteristics, AIAA J., 23, 1497 (1985) · Zbl 0571.76059 |
| [5] | MacCormack, R. W., The effect of viscosity in hypervelocity impact cratering, AIAA, Paper, 69, 354 (1969) |
| [6] | Kentzer, C. P., Reformulation of the method of characteristics for multidimensional flows, (Lecture Notes in Physics, Vol. 141 (1981), Springer: Springer New York), 242 |
| [7] | Kentzer, C. P., Discretization of boundary conditions on moving discontinuities, (Lecture Notes in Physics, Vol. 8 (1971), Springer: Springer New York), 108 · Zbl 0228.76099 |
| [8] | (Report LRG-65-T-38 (1965), Aerospace Library Services, Aerospace Corporation: Aerospace Library Services, Aerospace Corporation San Bernadino, California), Translated by K. N. Trirogoff |
| [9] | Varley, E.; Cumberbatch, E., Non-linear theory of wave-front propagation, J. Inst. Math. Appl., 1, 101 (1965) |
| [10] | Moretti, G., A physical approach to the numerical treatment of boundaries in gasdynamics, (Proc. Symp. Numerical Boundary Condition Procedures. Proc. Symp. Numerical Boundary Condition Procedures, NASA CP-2201 (1981)) |
| [11] | Parpia, I. H., Multidimensional time dependent method of characteristics, (Ph.D. Thesis (1986), Purdue University) · Zbl 0638.76085 |
| [12] | Lax, P. D.; Wendroff, B., Difference schemes with high order of accuracy for solving hyperbolic equations, Communs pure appl. Math., 17, 381 (1964) · Zbl 0233.65050 |
| [13] | Moretti, G.; Pandolfi, M., Critical study of calculations of subsonic flows in ducts, AIAA J., 19, 449 (1981) |
| [14] | Cuffel, R. F.; Back, L. H.; Massier, P. F., Transonic flowfield in a supersonic nozzle with small throat radius of curvature, AIAA J., 7, 1364 (1969) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
