Analytical treatment of two-dimensional supersonic flow. II. Flow with weak shocks

Abstract

A scheme of approximate solution is presented for the treatment of shock waves in the steady, plane flow of a perfect gas. It is based on the neglect of any entropy variations produced by the shocks and hence is applicable only when the shocks are weak. The method provides an extension of Friedrichs’s (1948) results for simple waves to wave-interaction regions. By an examination of the solution of the continuous-flow equations in the neighbourhood of a known shock wave it is shown how the downstream flow may be calculated without reference to the particular shock shape (§2). There are certain cases in which this approach fails and they are discussed by means of a typical example in §3.3. Once the downstream flow has been calculated, it is possible to set up general equations for the determination of the shock (§ 2). Examples of the solution of these equations for typical problems are given in §3. In §4 there is a brief discussion of the validity of using homentropic theory and estimates of the errors involved in the solution process are obtained.