A Conservative High Resolution Scheme for the Study of Gases and Liquids Homentropic Flows

In this paper a high-resolution explicit integration scheme is introduced and adopted to study the one-dimensional homentropic flow of a generic fluid, applicable to gaseous and liquid phase. The generally valid governing equations for one-dimensional homentropic flows are firstly introduced and, without forcing any assumption in relation to the nature of the fluid, an investigation of mathematical properties of the system of equations is given in order to derive the characteristic matrix and the system eigenvalue. Then, the Maxwell differential formulation of the fluid constitutive equations is introduced, with the purpose of providing a general state equation which retains its validity for both gases and liquids, and with the aim of expressing and explicitly calculating pressure, pressure derivative with respect to density and sound speed as functions of fluid bulk modulus. Starting from the differential formulation of the state equation, a high-resolution explicit integration scheme, based on conservative formulation of the governing equations for fluid flows, is then introduced and discussed. Finally, the well-known shock tube test is employed to study both liquid and gaseous flows, and the forthcoming numerical vs. analytical results comparison is used to assess the accuracy and the stability of the integration scheme.