Mathematical Aspects of Numerical Solution of Hyperbolic Systems
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€291.40
A01=A. Yu. Semenov
A01=A.G. Kulikovskii
A01=N.V. Pogorelov
advanced fluid mechanics
Approximate Riemann Problem Solvers
Author_A. Yu. Semenov
Author_A.G. Kulikovskii
Author_N.V. Pogorelov
Bow Shock
Category=PBKJ
Category=PBWR
Category=PDE
Category=PHD
Cd
CFL Number
Characteristic Velocity
conservation law solutions
electromagnetic wave propagation
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
Exact Riemann Problem Solver
Gas Dynamic
Gas Dynamic Equations
Godunov Method
higher order shock capturing schemes for MHD
HJ
Hugoniot Curve
Hyperbolic Systems
Ideal MHD
Integral Curve
Ionization Front
MHD Equation
MHD Flow
numerical analysis methods
partial differential equations
Quasilinear Hyperbolic System
Rarefaction Waves
Riemann Problem
Riemann Problem Solver
Rotational Discontinuities
Shallow Water Equations
shock wave modeling
Tangential Discontinuity
WENO Scheme
Product details
- ISBN 9780849306082
- Weight: 922g
- Dimensions: 156 x 234mm
- Publication Date: 21 Dec 2000
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena.
The authors also address a number of original "nonclassical" problems, such as shock wave propagation in rods and composite materials, ionization fronts in plasma, and electromagnetic shock waves in magnets. They show that if a small-scale, higher-order mathematical model results in oscillations of the discontinuity structure, the variety of admissible discontinuities can exhibit disperse behavior, including some with additional boundary conditions that do not follow from the hyperbolic conservation laws. Nonclassical problems are accompanied by a multiple nonuniqueness of solutions. The authors formulate several selection rules, which in some cases easily allow a correct, physically realizable choice.
This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes Mathematical Aspects of Numerical Solution of Hyperbolic Systems particularly valuable not only to those interested the development of numerical methods, but to physicists and engineers who strive to solve increasingly complicated nonlinear equations.
Kulikovskii, A.G.; Pogorelov, N.V.; Semenov, A. Yu.
