Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications

Non-oscillatory schemes for multidimensional Euler calculations with unstructured grids.- Finite-difference schemes with dissipation control joined to a generalization of van Leer flux splitting.- Computation of inviscid vortical flows in Piston engines.- Convexity in hyperbolic problems. Application to a discontinuous Galerkin method for the resolution of the polydimensional Euler equations.- Admissibility conditions for weak solutions of nonstrictly hyperbolic systems.- Uniformly second order convergent schemes for hyperbolic conservation laws including Leonard's approach.- High resolution finite volume schemes and computational aerodynamics.- A stability analysis of a Eulerian method for some surface gravity wave problems.- A quadrature approximation of the Boltzmann collision operator in axisymmetric geometry and its application to particle methods.- Boundary conditions for nonlinear hyperbolic systems of conservation laws.- Time-marching method to solve steady incompressible Navier-Stokes equations for laminar and turbulent flow.- On the finite velocity of wave motion modelled by nonlinear evolution equations.- Hyperbolic schemes for multi-component Euler equations.- Multigrid methods for solution of porous media multiphase flow equations.- A standard model of generic rotational degeneracy.- A numerical method for a system of equations modelling one-dimensional three-phase flow in a porous medium.- Nonuniqueness of solutions for Riemann problems.- Simple stability criteria for difference approximations of hyperbolic initial-boundary value problems.- Hyperbolic heat transfer problems with phase transitions.- Unsymmetric hyperbolic systems and almost incompressible flow.- Frequency decomposition multi-grid methods for hyperbolic problems.- Existence and uniquenessfor linear hyperbolic systems with unbounded coefficients.- A numerical method for computing viscous shock layers.- Solution of the Euler equations for unsteady, two-dimensional tranonic flow.- On some recent results for an explicit conservation law of mixed type in one dimension.- Qualitative behaviour of solutions for Riemann problems of conservation laws of mixed type.- Strongly nonlinear hyperbolic waves.- The structure of the Riemann solution for non-strictly hyperbolic conservation laws.- Detonation initiation due to shock wave-boundary interactions.- Nonconvex scalar conservation laws in one and two space dimensions.- Upwind schemes for the Navier-Stokes equations.- Normal reflection transmission of shock waves on a plane interface between two rubber-like media.- On the concept of weak solutions in the BV-space.- Numerical solution of the Euler equations used for simulation of 2D and 3D steady transonic flows.- Numerical schemes for the Euler equations in two dimensions without dimensional splitting.- Initial-boundary value problems for transonic equations in the unbounded domain.- Entropy weak solutions to nonlinear hyperbolic systems in nonconservation form.- A velocity-pressure model for elastodynamics.- Higher order accurate kinetic flux vector splitting method for Euler equations.- Monte Carlo finite difference methods for the solution of hyperbolic equations.- Numerical solution of flow equations. An aircraft designer's view.- Hypersonic blunt body computations including real gas effects.- Airfoil calculations in Cartesian grids.- Characteristic Galerkin methods for hyperbolic systems.- Numerical simulations of compressible hydrodynamic instabiltities with high resolution schemes.- On the "Flux-difference splitting" formulation.- On overdeterminedhyperbolic systems.- Runge-Kutta split-matrix method for the simulation of real gas hypersonic flows.- On some viscoelastic strongly damped nonlinear wave equations.- TVD schemes to compute compressible viscous flows on unstructured meshes.- Nonstationary shock wave generation in droplet vapour mixtures.- Nonlinear resonance phenomena for the Euler-equations coupled with chemical reaction-kinetics.- The design of algorithms for hypersurfaces moving with curvature-dependent speed.- Prediction of dispersive errors in numerical solutions of the Euler equations.- Numerical prediction of shock wave focusing phenomena in air with experimental verification.- Fundamental aspects of numerical methods for the propagation of multi-dimensional nonlinear waves in solids.- On a nonlinear telegraph equation with a free boundary.- "TVD" schemes for inhomogenous conservations laws.- The L1-Norm distinguishes the strictly hyperbolic from a non-strictly hyperbolic theory of the initial value problem for systems of conservation laws.- The Riemann problem with umbilic lines for wave propagation in isotropic elastic solids.- Random-choice based hybrid methods for one and two dimensional gas dynamics.- Some features of numerical algorithms for supersonic flow computation around wings of lifting vehicles.- Fully implicit high-resolution scheme for chemically reacting compressible flows.- Stability of semi-discrete approximations for hyperbolic initial-boundary-value problems: Stationary modes.- Some supraconvergent schemes for hyperbolic equations on irregular grids.- The homogeneous homentropic compression or expansion - A test case for analyzing Sod's operator-splitting.- Global existence of solutions for noncharacteristic mixed problems to nonlinear symmetric dissipative systems ofthe first order.- Stability of initial - boundary value problems for hyperbolic systems.- List of Participants and Authors.- Support and Sponsorship Acknowledgements.