A Stable, High-Order Extension to the Finite Volume With Exact Riemann Solvers (FIVER) Method

Geoffrey Main, Stanford University

The accurate and efficient computation of solutions to multi-material flow problems involving highly nonlinear fluid-structure interaction is important in many areas involving materials under extreme conditions. The Finite Volume method with Exact Riemann solvers (FIVER) scheme, developed recently, offers a common, robust approach for treating both fluid-fluid and fluid-structure interfaces within the Eulerian framework. However, like nearly all purely Eulerian methods for fluid-fluid and fluid-structure interaction problems, the original FIVER method is first-order space-accurate at material interfaces. For this reason, when equipped with a second-order flow solver, its attainable global order of accuracy is degraded from the value of 2 to 1.5. Hence, we will focus on presenting a simple extension of the original FIVER method which, for smooth problems, is capable of achieving an arbitrarily high order of accuracy throughout the computational domain, including at material interfaces. However, practical demonstrations will be discussed only for second-order spatial accuracy. For non-smooth multi-material flow and fluid-structure interaction problems, we will also discuss the nonlinear stability of ghost-fluid type methods and that of the extended FIVER method. We will present a framework for studying the nonlinear stability of these computational approaches, apply it to derive both theoretical and empirical stability results, and to construct limiters for the application of the higher-order extension of FIVER to problems with strong shocks and rarefactions in the neighborhood of material interfaces. Finally, numerical results will be presented for a variety of complex, highly nonlinear, multi-fluid and multi-fluid-structure interaction problems characterized by large deformations in order to highlight the remarkable performance of the extended FIVER method.

Abstract Author(s): Alex Main, Xianyi Zeng, and Charbel Farhat