Pressure-equilibrium-preserving and fully conservative discretization of compressible flow equations for real and thermally perfect gases
This addresses a long-standing problem of spurious pressure oscillations in compressible real-fluid simulations, which is critical for accurate modeling of supercritical and transcritical flows in engineering applications.
The paper proposes a novel numerical discretization for compressible real-fluid flows that preserves pressure equilibrium while maintaining full conservation of mass, momentum, and total energy. The method is validated on supercritical and transcritical flows using cubic equations of state, showing elimination of spurious pressure oscillations.
Numerical simulations of compressible real-fluid flows are notoriously plagued by spurious pressure oscillations arising in regions of abrupt flow variations. As a possible remedy, several numerical formulations enforce the pressure equilibrium condition for the compressible Euler equations, typically at the cost of spoiling the correct conservation of total energy or by overspecifying the thermodynamical variables. This study proposes for the first time a numerical discretization procedure which is able to discretely preserve the full conservation of the linear invariants (mass, momentum and total energy) and to exactly enforce the pressure equilibrium condition. The method also preserves the conservation of kinetic energy by convection, and is based on the specification of nonlinear numerical fluxes for mass and internal energy which depend on the details of the equation of state. Both thermally perfect and real gases with an arbitrary equation of state are considered, and a simplified approximate pressure equilibrium preserving formulation with excellent performances is also proposed. The effectiveness of the novel formulations is assessed through a series of numerical simulations in supercritical and transcritical conditions with some of the most popular cubic equations of state.