Implicit High-Order Compact Differencing Methods: Study of Convergence and Stability
Compact differencing can deliver high-order accuracy using only a limited span of stencils, but incurring a costly matrix in version. Hence, use of a stable implicit time discretizaton becomes favorable in order to offset the computation cost by allowing a large time step. A practical way to reduce the burden of inverting a large matrix from multidimensional problems is to split the implicit operator into a series of smaller operators. Undesirable consequences can surface, such as (1) loss of stability, and/or (2) loss of accuracy. Here, we propose a consistent implicit compact method and study the stability and accuracy of steady and unsteady solutions.
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