Engineering topics
Publications and source records attributed to Paullay, A. J..
Study of weak solutions of simple wave equation, inviscid Burgers equation, and Euler equations has resulted in technique for accurate prediction of shock waves occurring in inviscid supersonic flows.
Discontinuous, or weak, solutions of the wave equation, the inviscid form of Burgers equation, and the time-dependent, two-dimensional Euler equations are studied. A numerical method of second-order accuracy in two forms, differential and integral, is used to calculate the weak solutions of these equations for several initial value problems, including supersonic flow past a wedge, a double symmetric wedge, and a sphere. The effect of the computational mesh on the accuracy of computed weak solutions including shock waves and expansion phenomena is studied. Modifications to the finite-difference method are presented which aid in obtaining desired solutions for initial value problems in which the solutions are nonunique.
A technique is presented for computing multidimensional time-dependent flow fields that avoids much of the inefficiency typically found in finite difference calculations. The technique initially divides the flow field into regions, each containing a mesh of general quadrilateral cells chosen to provide spatial resolution of the local features of the flow. A finite difference operator of second order accuracy, consisting of a sequence of one-dimensional operators (each operating at near maximum Courant-Friedrich-Lewy number) is then constructed for each region. Numerical results illustrating the technique for inviscid flows about simple bodies that generate shock waves, embedded shock waves, and expansion fans are presented and compared with exact theory.