In the curved geometries, from the solution of the classical Riemann problem in the plane, the asymptotic solutions of the compressible Euler equation are presented. The explicit formulae are derived for the third order approximation of the generalized Riemann problem from the conventional setting of a planar shock-interface interaction.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
J. D. Anderson,Modern Compressible Flow with Historical Perspective 2nd Ed., McGraw-Hill, 1990.
A. Bourgeade and Ph. Le Floch and P. A. Raviart,An asymptotic expansion for the solution of the generalized Riemann problem, Ann. Inst. Henri Poincare, 6(1989), 437–480.
S. Chandrasekhar,Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1961.
H. Lamb,Hydrodynamics, Dover, New York, 1945.
L. Landau and E. Lifshitz,Fluid Mechanics, Addison Wesley, Reading, MA, 1959.
P. Lax,Weak Solutions of Nonlinear Hyperbolic Equations and Their Numerical Computations, Comm. Pure Appl. Math., 7(1954), 159.
P. Lax,Hyperbolic Systems of Conservation Laws II, Comm. Pure Appl. Math., 10(1957), 537–566.
E. E. Meshkov,Instability of a shock wave accelerated interface between two gases, NASA Tech. Trans., F-30(1970), 074.
E. Muller and B. Fryxell and D. Arnett,Instability and Clumping in SN 1987A, Astron. Astrophys., 251(1991), 505–514.
Lord Rayleigh,Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density, Scientific Papers, Cambridge Univ. Press, Cambridge, England, 1900.
R. D. Richtmyer,Taylor Instability in Shock Acceleration of Compressible Fluids, Comm. Pure Appl. Math., 13(1960), 297–319.
P. D. Roberts S. J. Rose and P. C. Thompson and R. J. Wright,The stability of multiple-shell ICF targets, J. Phys. D: Appl. Phys., 13(1980), 1957–1969.
Li Tatsien and Yu Wenci,Boundary Value Problem for Quasilinear Hyperbolic Systems, Duke University Mathematics Series, 1985.
G. I. Taylor,The Instability of Liquid Surfaces When Accelerated in a direction Perpendicular to Their Planes I, Proc. R Soc. London A, 201(1950), 192–196.
A. L. Velikovich and L. Phillips and J. Dahlburg,Analytic theory of the Richtmyer-Meshkov instability in compressible fluids, Phys. Rev. E, 1995.
About this article
Cite this article
Kim, J.H. The exact solution of the generalized Riemann problem in the curved geometries. Korean J. Comput. & Appl. Math. 7, 271 (2000). https://doi.org/10.1007/BF03012193
AMS Mathematics Subject Classification
Key word and phrases
- Euler equation
- asymptotic expansion
- generalized Riemann problem