Group Research Teaching Activity

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.

 

 

(a) Extended MUSCL scheme

 

(b) Extended Godunov scheme

 

Figure 1. Riemann problem of solid-water. An elastic wave and a plastic wave travel towards left, and a shock propagates to the right. Solid line -- exact solution, cirlces -- numerical solution.

 

 

 

(a) Explosion-steel-water-gas system

(b) A shock propagates in steel

 

map

(c) Wave travels in steel and water

 

(d) Zones of spallation in steel and cavitation in water
 

Figure 2. Simulation of wave, spallation, and cavitation in a gas-water-solid system.

 

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.