Download or read book Space-time Methods for Hyperbolic Conservation Laws written by and published by . This book was released on 1996 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two challenges for computational fluid dynamics are problems that involve wave propagation over long times and problems with a wide range of amplitude scales. An example with both of these characteristics is the propagation and generation of acoustic waves, where the mean-flow amplitude scales are typically orders-of-magnitude larger than those of the generated acoustics. Other examples include vortex evolution and the direct simulation of turbulence. All these problems require greater than second-order accuracy, whereas for nonlinear equations, most current methods are at best second- order accurate. Of the higher-order (greater than second-order) methods that exist, most are tailored to high-spatial resolution, coupled with time integrators that are only second or third-order accurate. But for wave phenomena, time accuracy is as important as spatial accuracy. One property of successful second-order methods is that they attempt to be faithful to the physics of hyperbolic problems. To develop higher-order methods, particularly for unsteady problems, it is tempting to violate this philosophy. Typically, higher accuracy is obtained by increasing the size of the update stencil. Instead our aim is to develop time-accurate methods that minimize the size of the update stencil. The approach in this study is strongly motivated by the physics of hyperbolic conservation laws. Specifically, we insist that a numerical method's discrete zone of dependence should only be slightly larger (for stability) than the physical zone of dependence. A time-accurate method has been developed that is based on the Discontinuous Galerkin method. In deriving the method, the idea of compactness has been strictly followed. That is, that the discrete domain of dependence should contain a minimum amount of data outside of the physical domain of dependence. For any order-of-accuracy, the method is stable for Courant numbers less than 1, satisfies an entropy condition, and a minimization property.