Stability analysis of space-time finite integration schemes

Abstract

[Purpose]– The purpose of this paper is to examine the numerical stability of a space-time finite integration (FI) method. A symmetric correction is proposed to give an accurate constitutive relation at the subgrid connections. [Design/methodology/approach]– A scheme for the numerical stability analysis of the space-time FI method is presented, where the growth rate of instability is evaluated by a numerical eigenvalue analysis formulated from an explicit time-marching scheme. [Findings]– The 3D and 4D subgrid schemes using the space-time FI method are conditionally stable, where a symmetric correction does not induce numerical instability. The staircase-type 4D space-time subgrid allows a larger time-step than the straight-type subgrid. [Originality/value]– The numerical stability of space-time FI method is proven by an eigenvalue analysis, which provides 3D and 4D stable subgrid schemes.