Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems

Free boundary problems in shock reflection/diffraction and related transonic flow problems.

Shock waves are steep wavefronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematic...

Quasi - One - Dimensional Riemann Problems

We study two-dimensional Riemann problems with piecewise constant data. We identify a class of two-dimensional systems, including many standard equations of compressible ow, which are simpliied by a transformation to similarity variables. For equations in this class, a two-dimensional Riemann problem with sectorially constant data becomes a boundary-value problem in the nite plane. For data lea...

Application of the Boundary Element Method to two Dimensional Dynamic Problems of Saturated Porous Media

Two-Dimensional Riemann Problems for the Compressible Euler System∗∗

Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult, but a viable alternative remains missing. We list merits of one-dimensional Riemann problems and compare them with those for the current two-dimensional Riemann problems, to illustrate their worthiness. We approach twodimensional Riemann problems via the methodology promoted by Andy Majda i...

Application of the Boundary Element Method to two Dimensional Dynamic Problems of Saturated Porous Media