Finite Volume Methods for Hyperbolic ProblemsCambridge University Press, 26 de ago. de 2002 This book, first published in 2002, 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 then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and 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. |
Termos e frases comuns
2shock accuracy acoustics equations advection equation algorithms approach approximate Riemann boundary conditions Burgers canbe cell averages Chapter CLAWPACK coefficient compute conservation law consider constantcoefficient contact discontinuity convergence dambreak define density derived determine dimension eigenvalues eigenvectors entropy condition error Euler equations example finite volume methods firstorder flow fluctuations fluid flux function formula gives Godunov’s method grid cell hence higherorder highresolution methods hyperbolic equations hyperbolic system initial data integral curve interface inthe Jacobian matrix jump Lax–Wendroff method limiter linear system nonlinear systems Note numerical method obtain ofthe onedimensional oscillations physical propagating Rankine–Hugoniot rarefaction wave Riemann problem Riemann solution Riemann solver Runge–Kutta method satisfied secondorder accurate shallow water equations shock wave shown in Figure shows simply solving the Riemann source term space splitting systems of equations Taylor series total variation twodimensional upwind method vector velocity viscosity wavepropagation weak solution