Supercomputer implementation of finite element algorithms for high speed compressible flows. Progress report, period ending 30 June 1986

Technical Report · Sun Jun 01 00:00:00 EDT 1986

OSTI ID:7002906

Thornton, E A; Ramakrishnan, R

Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes.

• Research Organization: Old Dominion Univ., Norfolk, VA (USA)
• OSTI ID: 7002906
• Report Number(s): N-86-33043; NASA-CR-177065; NAS-1.26:177065; TRN: 87-002494
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
COMPRESSIBLE FLOW
FINITE ELEMENT METHOD
ALGORITHMS
COMPUTER CODES
MATHEMATICAL MODELS
SERIES EXPANSION
SUPERCOMPUTERS
THEORETICAL DATA
VISCOUS FLOW
COMPUTERS
DATA
DIGITAL COMPUTERS
FLUID FLOW
INFORMATION
MATHEMATICAL LOGIC
NUMERICAL DATA
NUMERICAL SOLUTION
420400* - Engineering- Heat Transfer & Fluid Flow