Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications

On the occasion of the International Conference on Nonlinear Hyperbolic Problems held in St. Etienne, France, 1986 it was decided to start a two years cycle of conferences on this very rapidly expanding branch of mathematics and it·s applications in Continuum Mechanics and Aerodynamics. The second conference toolc place in Aachen, FRG, March 14-18, 1988. The number of more than 200 participants from more than 20 countries all over the world and about 100 invited and contributed papers, well balanced between theory, numerical analysis and applications, do not leave any doubt that it was the right decision to start this cycle of conferences, of which the third will be organized in Sweden in 1990. ThiS volume contains sixty eight original papers presented at the conference, twenty two cif them dealing with the mathematical theory, e.g. existence, uniqueness, stability, behaviour of solutions, physical modelling by evolution equations. Twenty two articles in numerical analysis are concerned with stability and convergence to the physically relevant solutions such as schemes especially deviced for treating shoclcs, contact discontinuities and artificial boundaries. Twenty four papers contain multidimensional computational applications to nonlinear waves in solids, flow through porous media and compressible fluid flow including shoclcs, real gas effects, multiphase phenomena, chemical reactions etc. The editors and organizers of the Second International Conference on Hyperbolic Problems would lilce to thanlc the Scientific Committee for the generous support of recommending invited lectures and selecting the contributed papers of the conference.

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 uniqueness for 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 overdetermined hyperbolic 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 of the first order.- Stability of initial ― boundary value problems for hyperbolic systems.- List of Participants and Authors.- Support and Sponsorship Acknowledgements.