A general linear method approach to the design and optimization of efficient, accurate, and easily implemented time-stepping methods in CFD

In simulations of fluid motion time accuracy has proven to be elusive. We seek highly accurate methods with strong enough stability properties deal the richness scales many flows. These must also easy implement within current complex, possibly legacy codes. Herein we develop, analyze and test new stepping addressing these two issues goal accelerating development needs applications. The are created by introducing inexpensive pre-filtering post-filtering steps popular which have been implemented tested existing show that a multistep or multi-stage method results in both multiple stages: general linear (GLMs). utilize well studied GLMs understand filtered method, design optimal filters for time-stepping methods. present several embedded families high low cognitive complexity excellent properties. Numerical tests presented, including ones finding failure points some Among presented is novel pair alternating Implicit Euler induces third order, A-stable, error inhibiting scheme shown particularly effective.