Abstract
A control-volume -based finite element method with a new formulation for the convecting integration-point velocity for the implicit solution of unsteady compressible and incompressible flows is presented in this article. The method creates a strong coupling between pressure and velocity in incompressible flow on a colocated grid. A pressure-based approach is used to generalize the method for both compressible and incompressible flows. Several quasi-one-dimensional test problems provide validation of the method for Mach numbers ranging from very incompressible flow to supersonic flow with no penalty in accuracy or rate of convergence. Strong shock waves are captured without introducing artificial viscosity.
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