Shock and Wave in Multiphase Media

Exact solutions for Riemann problems for system of vaccum, gas, water, and solid (elastic-plastic), such as gas-water, water-solid, were constructed and solved, and on this basis, the original MUSCL scheme by van Leer for continuous gas flows was extedned to flows of coupling systems of such media. The following figures are examples.

Reference

H. S. Tang and F. Sotiropoulos, A second-order Godunov method for wave problems in coupled solid-water-gas systems, J. Comput. Phys., 151(1999), 790-815.

H. S. Tang, A second-order Godunov method for computing solutions to wave motion and fracture problems in a hydro-elasto-plastic medium. Chinese J. Numer. Math. Appl., 21(1999), 69—82.(Full Text PDF)

H. S. Tang and D. Huang, A second-order accurate capturing scheme for 1D inviscid flows of gas and water with vacuum zones, J. Comput. Phys, 128(1996), 301-318.