Linearly Implicit Rosenbrock Methods for Unsteady Flow Simulation

Abstract

In this work we present details on the implementation of linear Rosenbrock-type methods and their application to unsteady flow problems. Over the recent years, especially in the field of high order methods, diagonally implicit Runge-Kutta (DIRK) methods gained popularity. However, linear Rosenbrock methods are an easier to implement and use alternative. Their implementation requires little more than what is already commonly available in most flow solvers. We present results covering DNS, LES and URANS applications and show that when combined with a second order finite volume method, second order Rosenbrock schemes provide sufficient accuracy. In particular, the ROS2 scheme shows simultaneously increased performance and accuracy compared to the popular second order backward differentiation formula (BDF2). At the same time, it consistently outperforms similar DIRK schemes in our implementation. As an addition to a legacy FV solver, Rosenbrock methods can increase performance and accuracy and extend its range of applicability and lifespan.