When a shock front in unsteady compressible flow is moving along an inclined ramp, the incident shock will be reflected by the ramp, as it moves forward. In the process of reflection, various reflected wave pattern may occur depending on the slope of the ramp and the strength of the incident shock [14, 23]. This problem is one of the most important multidimensional prototype problems in gas dyn...

Stochastic methods offer an attractively simple solution to complex transport-controlled problems, and have a wide range of physical, chemical, and biological applications. Stochastic methods do not suffer from the numerical diffusion that plagues grid-based methods, but they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce some ideas and algorithms t...