A novel extension of GS4-1 time integrator to fluid dynamics type non-linear problems with illustrations to Burgers’ equation

Purpose – The purpose of this paper is to describe how a generalized single-system-single-solve (GS4-1) computational framework, previously developed for linear first order transient systems, can be properly extended for use in nonlinear counterparts, with particular applications to time dependent Burgers’ equation, which is well-known to serve as a simplified model of fluid dynamics, for illustrations of the essential concepts. Design/methodology/approach – The framework permits, for a very general family of time integrators where traditional methods are a subset, much needed desirable features including second order time accuracy, robustness and unconditional stability, zero-order overshoot behavior, and additionally, a selective control of high frequency damping for both the primary variable and its time derivative. The latter, which is a new, key desirable feature not available in past/existing methods to-date, allows for different amounts of high frequency damping for both the primary variable and it...