Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Three-dimensional implicit approximately factored schemes for the equations of gasdynamics

Thesis/Dissertation ·
OSTI ID:6930529
For reasons of efficiency and limitations in computing power, implicit approximate factorization schemes (or in particular, alternating direction implicit (ADI) schemes have been used in multi-dimensional applications. However, analysis indicates that although the ADI scheme for two dimensions is unconditionally stable for a model convection equation, the same procedure in three dimensions leads to numerical instability. In this dissertation, the stability properties of conventional ADI schemes and various implicit two-factored schemes are examined. The immediate objective is to develop an efficient, unconditionally stable, implicit algorithm for numerically solving the equations of gasdynamics in three dimensions. The analysis shows that only conditional stability is obtained by the addition of numerical dissipation to the Beam and Warming algorithm. However, unconditionally stable schemes can be constructed through the use of two implicit factors with the proper space differencing for each spatial direction. This implicit, two-factored, flux-split scheme (TFS) is a second-order accurate in space, first- or second-order accurate in time, non-iterative and vectorizable on supercomputers. The RFS scheme was applied to both steady and unsteady three-dimensional flows using a CRAY II supercomputer and post-processed by the IRIS work station for visualization.
Research Organization:
Stanford Univ., CA (USA)
OSTI ID:
6930529
Country of Publication:
United States
Language:
English