Sharp interface simulations with Local Mesh Refinement for multi-material dynamics in strongly shocked flows

• Published in: Computers & fluids Vol. 39; no. 9; pp. 1456 - 1479
• Main Authors: Sambasivan, Shiv Kumar, UdayKumar, H.S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-10-2010; Elsevier
• Subjects: Adaptive Mesh Refinement; Cartesian grid methods; Compressible flows; shock and detonation phenomena; Compressible multi-material flows; Compressible multiphase flows; Computational fluid dynamics; Computational methods in fluid dynamics; Computer simulation; Exact sciences and technology; Finite element method; Fluid dynamics; Fluid flow; Fluids; Fundamental areas of phenomenology (including applications); Ghost Fluid Method (GFM); Local Mesh Refinement; Mathematical models; Physics; Riemann solver; Sharp Interface Methods; Shock waves; Shock-interface interactions; Shock-wave interactions and shock effects; Compressible multiphase flows; Cartesian grid methods; Shock-interface interactions; Sharp Interface Methods; Compressible multi-material flows; Adaptive Mesh Refinement; Ghost Fluid Method (GFM); Local Mesh Refinement; Compressible fluid; Wave diffraction; Projectiles; Refinement method; Digital simulation; Particle suspension; Adaptive method; Shock waves; Bubbles; Fluid solid interface; Fluid-fluid interfaces; Droplets; Modelling; Interactions; Mesh generation
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2010.04.014

Shock waves interacting with multi-material interfaces in compressible flows result in complex shock diffraction patterns involving total or partial reflection, refraction and transmission of the impinging shock wave. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with levelset interface tracking is attractive. In this regard, a unified Riemann solver based Ghost Fluid Method (GFM) is developed to accurately resolve and represent the embedded solid and fluid object(s) in high speed compressible multiphase flows. In addition, the Riemann solver based GFM approach is augmented with a quadtree (octree in three-dimensions) based Local Mesh Refinement (LMR) technique for efficient and high fidelity computations involving strong shock interactions. The paper reports on a conservative formulation for accurate calculation of ENO-based numerical fluxes at the fine-coarse mesh boundaries. The numerical examples presented in this paper clearly demonstrate that the methodology produces accurate benchmark solutions and effectively captures fine structures in the flow field.