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The two-dimensional Riemann problem in gas dynamics (Hardcover)
Loot Price: R5,144
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The two-dimensional Riemann problem in gas dynamics (Hardcover)
Series: Monographs and Surveys in Pure and Applied Mathematics
Expected to ship within 12 - 17 working days
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The Riemann problem is the most fundamental problem in the entire
field of non-linear hyperbolic conservation laws. Since first posed
and solved in 1860, great progress has been achieved in the
one-dimensional case. However, the two-dimensional case is
substantially different. Although research interest in it has
lasted more than a century, it has yielded almost no analytical
demonstration. It remains a great challenge for mathematicians.
This volume presents work on the two-dimensional Riemann problem
carried out over the last 20 years by a Chinese group. The authors
explore four models: scalar conservation laws, compressible Euler
equations, zero-pressure gas dynamics, and pressure-gradient
equations. They use the method of generalized characteristic
analysis plus numerical experiments to demonstrate the elementary
field interaction patterns of shocks, rarefaction waves, and slip
lines. They also discover a most interesting feature for
zero-pressure gas dynamics: a new kind of elementary wave appearing
in the interaction of slip lines-a weighted Dirac delta shock of
the density function. The Two-Dimensional Riemann Problem in Gas
Dynamics establishes the rigorous mathematical theory of
delta-shocks and Mach reflection-like patterns for zero-pressure
gas dynamics, clarifies the boundaries of interaction of elementary
waves, demonstrates the interesting spatial interaction of slip
lines, and proposes a series of open problems. With applications
ranging from engineering to astrophysics, and as the first book to
examine the two-dimensional Riemann problem, this volume will prove
fascinating to mathematicians and hold great interest for
physicists and engineers.
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