Finite Volume Methods for Hyperbolic ProblemsCambridge University Press, 26 ago 2002 - 558 pagine This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws). These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. Source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods. |
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Parole e frasi comuni
acoustics equations advection equation algorithm approach boundary conditions cell average Chapter characteristic CLAWPACK coefficient compute conservation law consider constant-coefficient contact discontinuity convergence Courant number define density derived differential equation discussed in Section domain eigenvalues eigenvectors entropy entropy condition Euler equations example finite volume methods first-order flow fluctuations fluid flux function formula fractional-step method gives Godunov's method grid cell hence high-resolution methods Hugoniot hyperbolic equations hyperbolic system initial data integral curve Jacobian matrix jump Lax-Wendroff method limiter linear system nonlinear systems Note numerical methods obtain one-dimensional piecewise constant q₁ rarefaction wave Riemann problem Riemann solution Riemann solver satisfied shallow water equations shock wave shown in Figure simply smooth solving the Riemann source term splitting step systems of equations Taylor series u₁ upwind method variable-coefficient variables vector velocity viscosity wave speeds waves propagating weak solution ΔΙ