A Variational Principle for Unsteady Compressible Flow

Abstract

A novel variational (weak) form of governing equations for nonlinear unsteady compressible flow is derived based on first physical principles. Mathematical proof of equivalence of the strong form and the weak form is presented. This variational form is derived with the goal of eventually coupling it with the structural dynamic governing equation to address fluid–structure interaction problems. Therefore, analogy with the weak form of structural dynamics equations is essential. In this regard, an important observation on the distinction between the variational form of the governing equations in fluid and structural mechanics is made. Developing a numerical solution from a variational form is less tedious than a strong form of equations. Finally, the numerical results based on the new variational formulation and the analytical solution for parallel flow are compared.