An Efficient, Semi-implicit Pressure-based Scheme Employing a High-resolution Finitie Element Method for Simulating Transient and Steady, Inviscid and Viscous, Compressible Flows on Unstructured Grids

Technical Report · Tue Apr 01 00:00:00 EST 2003

DOI:https://doi.org/10.2172/910726· OSTI ID:910726

Martineau, Richard C; Berry, Ray A

A new semi-implicit pressure-based Computational Fluid Dynamics (CFD) scheme for simulating a wide range of transient and steady, inviscid and viscous compressible flow on unstructured finite elements is presented here. This new CFD scheme, termed the PCICEFEM (Pressure-Corrected ICE-Finite Element Method) scheme, is composed of three computational phases, an explicit predictor, an elliptic pressure Poisson solution, and a semiimplicit pressure-correction of the flow variables. The PCICE-FEM scheme is capable of second-order temporal accuracy by incorporating a combination of a time-weighted form of the two-step Taylor-Galerkin Finite Element Method scheme as an explicit predictor for the balance of momentum equations and the finite element form of a time-weighted trapezoid rule method for the semi-implicit form of the governing hydrodynamic equations. Second-order spatial accuracy is accomplished by linear unstructured finite element discretization. The PCICE-FEM scheme employs Flux-Corrected Transport as a high-resolution filter for shock capturing. The scheme is capable of simulating flows from the nearly incompressible to the high supersonic flow regimes. The PCICE-FEM scheme represents an advancement in mass-momentum coupled, pressurebased schemes. The governing hydrodynamic equations for this scheme are the conservative form of the balance of momentum equations (Navier-Stokes), mass conservation equation, and total energy equation. An operator splitting process is performed along explicit and implicit operators of the semi-implicit governing equations to render the PCICE-FEM scheme in the class of predictor-corrector schemes. The complete set of semi-implicit governing equations in the PCICE-FEM scheme are cast in this form, an explicit predictor phase and a semi-implicit pressure-correction phase with the elliptic pressure Poisson solution coupling the predictor-corrector phases. The result of this predictor-corrector formulation is that the pressure Poisson equation in the PCICE-FEM scheme is provided with sufficient internal energy information to avoid iteration. The ability of the PCICE-FEM scheme to accurately and efficiently simulate a wide variety of inviscid and viscous compressible flows is demonstrated here.

• Research Organization: Idaho National Lab. (INL), Idaho Falls, ID (United States)
• Sponsoring Organization: DOE - SC
• DOE Contract Number: DE-AC07-99ID-13727
• OSTI ID: 910726
• Report Number(s): INEEL/EXT-03-00490; TRN: US200802%%103
• Country of Publication: United States
• Language: English

Related Subjects

99 - GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ACCURACY
COMPRESSIBLE FLOW
COMPUTERIZED SIMULATION
FINITE ELEMENT METHOD
FLUID MECHANICS
HYDRODYNAMICS
POISSON EQUATION
SUPERSONIC FLOW
TRANSIENTS
TRANSPORT
Compressed flows
High-Resolution finite element
Inviscid
Semi-Implicit Pressure-Based Scheme
Viscous