Accuracy and stability of time-split finite-difference schemesIn a recently published work by Abarbanel and Gottlieb (1980), a new class of explicit time-split algorithms designed for application to the compressible Navier-Stokes equations was developed. These algorithms, which utilize locally-one-dimensional (LOD) spatial steps, were shown to possess stability characteristics superior to those of other time-split schemes. In the present work, the properties of an implicit LOD method, analogous to the Abarbanel-Gottlieb algorithm, are examined using the two-dimensional heat conduction equation as the test problem. Both temporal and spatial inconsistencies inherent in the scheme are identified, and a new consistent, implicit splitting approach is developed and applied to the linear Burgers' equation. The relationship between this new method and other time-split implicit schemes is explained and stability problems encountered with the method in three dimensions are discussed.
Document ID
19810053132
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Dwoyer, D. L. (NASA Langley Research Center Hampton, VA, United States)
Thames, F. C. (NASA Langley Research Center Hampton, Va., United States)