c 2008 Society for Industrial and Applied Mathematics SIAM J. SCI. COMPUT. Vol. 30, No. 3, pp. 1105–1130 THE MODIFIED GHOST FLUID METHOD FOR COUPLING OF FLUID AND STRUCTURE CONSTITUTED WITH HYDRO-ELASTO-PLASTIC EQUATION OF STATE∗ T. G. LIU† , W. F. XIE‡ , AND B. C. KHOO§ Abstract. In this work, the modified ghost fluid method (MGFM) [T. G. Liu, B. C. Khoo, and K. S. Yeo, J. Comput. Phys., 190 (2003), pp. 651–681] is further developed and applied to treat the compressible fluid-compressible structure coupling. To facilitate theoretical analysis, the structure is modeled as elastic-plastic material with perfect plasticity and constituted with the hydro-elastoplastic equation of state [H. S. Tang and F. Sotiropoulos, J. Comput. Phys., 151 (1999), pp. 790– 815] under strong impact. This results in the coupled compressible fluid-compressible structure system which is fully hyperbolic. To understand the effect of structure deformation on the interfacial and flow status, the compressible fluid-compressible structure Riemann problem is analyzed in the consideration of material deformation with an approximate Riemann problem solver proposed to take into account the effect of material elastic-plastic deformation. We clearly show the ghost fluid method can be applied to treat the flow-deformable structure coupling under strong impact provided that a proper Riemann problem solver is used to predict the ghost fluid states. And the resultant MGFM can work effectively and efficiently in such situations. Various examples are presented to validate and support the conclusions reached. Key words. modified ghost fluid method, GFM Riemann problem, approximate Riemann problem solver, fluid-compressible structure coupling AMS subject classifications. 35L45, 65C20, 76T10 DOI. 10.1137/050647013 1. Introduction. The simulation of multimedium compressible flow is still a very challenging topic, especially if the density ratio of two media is very large or one of the media is constituted with a stiff equation of state (EOS). This is because commonly used high resolution schemes for compressible flows such as total-variation-diminishing (TVD) schemes [8, 9] and essentially nonoscillatory (ENO) schemes [11, 10, 24], which work efficiently for pure-medium compressible flows, can run into unexpected difficulties due to numerical oscillations generated in the vicinity of material interfaces. Such oscillations (especially pressure oscillations) are analyzed mathematically by Karni [12] and Abgrall and Karni [2]. To suppress unphysical oscillations, various techniques have been developed [12, 2, 1, 25, 23, 18, 22, 30, 6, 5, 3, 33, 16]. Among those techniques, the ghost fluid method (GFM) [6] provided a flexible way for treatment of multimedium flows. The key point of a GFM-based algorithm is to properly define ghost fluids, which is the only difference among various GFM-based algorithms [20, 2, 6, 5, 3, 33, 16]. One main advantage of the GFM-based algorithm is ∗ Received by the editors December 8, 2005; accepted for publication (in revised form) May 21, 2007; published electronically March 21, 2008. http://www.siam.org/journals/sisc/30-3/64701.html † Institute of High Performance Computing, The Capricorn, Science Park II, Singapore 117528, Singapore. Current address: Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083, People’s Republic of China (
[email protected]). ‡ Institute of High Performance Computing, The Capricorn, Science Park II, Singapore 117528, Singapore. Current address: Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544 (
[email protected]). § Department of