Analysis of the Boundary Problem with the Preference of Mass Flow

Abstract

We work with the numerical solution of the turbulent compressible gas flow, and we focus on the numerical solution of these equations, and on the boundary conditions, particularly on the outlet boundary condition with the preference of given mass flow. Usually, the boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but it has a huge impact on the solution in the whole studied area, especially for the non-stationary flow. The boundary condition with the preference of mass flow is sometimes being implemented with the use of some iterative process, guessing the correct values (for the pressure, density, velocity) in order to match the given mass flow through the boundary. In our approach we try to be as exact as possible, using our own original procedures. We follow the exact solution of the initial-value problem for the system of hyperbolic partial differential equations. This complicated problem is modified at the close vicinity of boundary, where the conservation laws are supplied with the additional boundary conditions. We complement the boundary problem suitably, and we show the analysis of the resulting uniquely-solvable modified Riemann problem.The resulting algorithm was coded and used within our own developed code for the solution of the compressible gas flow (the Euler, NS, and RANS equations). The examples show good behaviour of the analyzed boundary condition.