The pressure-corrected ICE finite element method for compressible flows on unstructured meshes

A new implicit continuous-fluid Eulerian (ICE) scheme for simulating a wide range of transient and steady, inviscid and viscous compressible flows on unstructured finite elements is presented. This new computational fluid dynamics scheme, termed the pressure-corrected ICE-finite element method (PCICE-FEM), represents an advancement in mass–momentum coupled, pressure-based schemes. The governing hydrodynamic equations for this scheme consist of the conservative forms of the momentum balance (Navier–Stokes), mass conservation, and total energy equations. The PCICE-FEM scheme is developed as a predictor–corrector scheme by performing a fractional-step splitting of the semi-implicit temporal discretization of the governing equations into an explicit predictor phase and a semi-implicit pressure-correction phase coupled by a pressure Poisson solution. The result of this predictor–corrector formulation is that the pressure Poisson equation is provided with sufficient internal energy information to avoid iteration with the semi-implicit pressure-correction equations. The PCICE-FEM scheme combines a modified form of the two-step Taylor–Galerkin FEM scheme as an explicit predictor for the fractional momentum equations and a time-weighted FEM method for the semi-implicit form of the mass conservation and the total energy equations. The PCICE-FEM scheme employs flux-corrected transport (FCT) as a high-resolution filter for shock capturing. The ability of the PCICE-FEM scheme to accurately and efficiently simulate a wide variety of flows from nearly incompressible to highly compressible is demonstrated.