An interface capturing method for the simulation of multi-phase compressible flows

• Published in: Journal of computational physics Vol. 229; no. 19; pp. 7411 - 7439
• Main Authors: Shukla, Ratnesh K., Pantano, Carlos, Freund, Jonathan B.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.09.2010; Elsevier
• Subjects: Compressible flow; Compressing; Computational techniques; Computer simulation; Contact; Diffusion; Equations of state; Exact sciences and technology; Interface capturing; Mathematical analysis; Mathematical methods in physics; Mathematical models; Multi-phase flows; Phase field models; Physics; Shocks; Multi-phase flows; Phase field models; Interface capturing; Shocks; Collapse; Riemann problem; High density; Riemann metric; Calculation methods; Weak convergence; Equations of state; Three dimensional flow; Models; Calculation; Diffusion; Compressible flow
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.06.025

A novel finite-volume interface (contact) capturing method is presented for simulation of multi-component compressible flows with high density ratios and strong shocks. In addition, the materials on the two sides of interfaces can have significantly different equations of state. Material boundaries are identified through an interface function, which is solved in concert with the governing equations on the same mesh. For long simulations, the method relies on an interface compression technique that constrains the thickness of the diffused interface to a few grid cells throughout the simulation. This is done in the spirit of shock-capturing schemes, for which numerical dissipation effectively preserves a sharp but mesh-representable shock profile. For contact capturing, the formulation is modified so that interface representations remain sharp like captured shocks, countering their tendency to diffuse via the same numerical diffusion needed for shock-capturing. Special techniques for accurate and robust computation of interface normals and derivatives of the interface function are developed. The interface compression method is coupled to a shock-capturing compressible flow solver in a way that avoids the spurious oscillations that typically develop at material boundaries. Convergence to weak solutions of the governing equations is proved for the new contact capturing approach. Comparisons with exact Riemann problems for model one-dimensional multi-material flows show that the interface compression technique is accurate. The method employs Cartesian product stencils and, therefore, there is no inherent obstacles in multiple dimensions. Examples of two- and three-dimensional flows are also presented, including a demonstration with significantly disparate equations of state: a shock induced collapse of three-dimensional van der Waal’s bubbles (air) in a stiffened equation of state liquid (water) adjacent to a Mie-Grüneisen equation of state wall (copper).