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Title: 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

Abstract

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 processmore » 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.« less

Authors:
;
Publication Date:
Research Org.:
Idaho National Laboratory (INL)
Sponsoring Org.:
DOE - SC
OSTI Identifier:
910726
Report Number(s):
INEEL/EXT-03-00490
TRN: US200802%%103
DOE Contract Number:  
DE-AC07-99ID-13727
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Richard C. Martineau, and Ray A. Berry. 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. United States: N. p., 2003. Web. doi:10.2172/910726.
Richard C. Martineau, & Ray A. Berry. 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. United States. doi:10.2172/910726.
Richard C. Martineau, and Ray A. Berry. Tue . "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". United States. doi:10.2172/910726. https://www.osti.gov/servlets/purl/910726.
@article{osti_910726,
title = {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},
author = {Richard C. Martineau and Ray A. Berry},
abstractNote = {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.},
doi = {10.2172/910726},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2003},
month = {4}
}

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