Ebook: Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications: Proceedings of the Second International Conference on Nonlinear Hyperbolic Problems, Aachen, FRG, March 14 to 18, 1988

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.

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Content:
Front Matter....Pages I-X
Non-Oscillatory Schemes for Multidimensional Euler Calculations with Unstructured Grids....Pages 1-10
Finite-Difference Schemes with Dissipation Control Joined to a Generalization of Van Leer Flux Splitting....Pages 11-20
Computation of Inviscid Vortical Flows in Piston Engines....Pages 21-30
Convexity in Hyperbolic Problems. Application to a Discontinuous Galerkin Method for the Resolution of the Polydimensional Euler Equations....Pages 31-42
Admissibility Conditions for Weak Solutions of Nonstrictly Hyperbolic Systems....Pages 43-50
Uniformly Second Order Convergent Schemes for Hyperbolic Conservation Laws Including Leonard’s Approach....Pages 51-62
High Resolution Finite Volume Schemes and Computational Aerodynamics....Pages 63-74
A Stability Analysis of a Eulerian Method for Some Surface Gravity Wave Problems....Pages 75-84
A Quadrature Approximation of the Boltzmann Collision Operator in Axisymmetric Geometry and Its Application to Particle Methods....Pages 85-95
Boundary Conditions for Nonlinear Hyperbolic Systems of Conservation Laws....Pages 96-104
Time-Marching Method to Solve Steady Incompressible Navier-Stokes Equations for Laminar and Turbulent Flow....Pages 105-114
On the Finite Velocity of Wave Motion Modelled by Nonlinear Evolution Equations....Pages 115-127
Hyperbolic Schemes for Multi-Component Euler Equations....Pages 128-138
Multigrid Methods for the Solution of Porous Media Multiphase Flow Equations....Pages 139-148
A standard model of generic rotational degeneracy....Pages 149-158
A Numerical Method for a System of Equations Modelling one-Dimensional three-Phase Flow in a Porous Medium....Pages 159-168
Nonuniqueness of Solutions for Riemann Problems....Pages 169-178
Simple Stability Criteria for Difference Approximations of Hyperbolic Initial-Boundary Value Problems....Pages 179-185
Hyperbolic Heat Transfer Problems with Phase Transitions....Pages 186-192
Unsymmetric Hyperbolic Systems and Almost Incompressible Flow....Pages 193-208
Frequency Decomposition Multi-Grid Methods for Hyperbolic Problems....Pages 209-217
Existence and Uniqueness for Linear Hyperbolic Systems with Unbounded Coefficients....Pages 218-219
A Numerical Method for Computing Viscous Shock Layers....Pages 220-229
Solution of the Euler Equations for Unsteady, Two-Dimensional, Transonic Flow....Pages 230-237
On some Recent Results for an Explicit Conservation Law of Mixed Type in One Dimension....Pages 238-245
Qualitative behavior of solutions for Riemann problems of conservation laws of mixed type....Pages 246-256
Strongly Nonlinear Hyperbolic Waves....Pages 257-268
The Structure of the Riemann Solution for Non-Strictly Hyperbolic Conservation Laws....Pages 269-278
Detonation Initiation Due to Shock Wave-Boundary Interactions....Pages 279-288
Nonconvex Scalar Conservation Laws in One and Two Space Dimensions....Pages 289-299
Upwind Schemes for the Navier-Stokes Equations....Pages 300-309
Normal Reflection Transmission of Shocks Waves on a Plane Interface between Two Rubber-Like Media....Pages 310-319
On the Concept of Weak Solutions in the BV-Space....Pages 320-328
Numerical Solution of the Euler Equations Used for Simulation of 2D and 3D Steady Transonic Flows....Pages 329-341
Numerical schemes for the Euler equations in two space dimensions without dimensional splitting....Pages 342-352
Initial-Boundary Value Problems for Transonic Equations in the Unbounded Domain....Pages 353-361
Entropy Weak Solutions to Nonlinear Hyperbolic Systems in Nonconservation Form....Pages 362-373
A Velocity-Pressure Model for Elastodynamics....Pages 374-383
Higher Order Accurate Kinetic Flux Vector Splitting Method for Euler Equations....Pages 384-392
Monte Carlo Finite Difference Methods for the Solution of Hyperbolic Equations....Pages 393-402
Numerical Solution of Flow Equations an Aircraft Designer’s View....Pages 403-412
Hypersonic Blunt Body Computations Including Real Gas Effects....Pages 413-422
Airfoil Calculations in Cartesian Grids....Pages 423-434
Characteristic Galerkin Methods for Hyperbolic Systems....Pages 435-455
Numerical Simulations of Compressible Hydrodynamic Instabiltities with High Resolution Schemes....Pages 456-465
On the “Flux-Difference Splitting” Formulation....Pages 466-481
On Overdetermined Hyperbolic Systems....Pages 482-488
Runge-Kutta Split-Matrix Method for the Simulation of Real Gas Hypersonic Flows....Pages 489-498
On Some Viscoelastic Strongly Damped Nonlinear Wave Equations....Pages 499-509
TVD Schemes to Compute Compressible Viscous Flows on Unstructured Meshes....Pages 510-520
Nonstationary Shock Wave Generation in Droplet Vapour Mixtures....Pages 521-529
Nonlinear Resonance Phenomena for the Euler — Equations Coupled with Chemical Reaction — Kinetics....Pages 530-543
The Design of Algorithms for Hypersurfaces Mowing with Curvature-Dependent Speed....Pages 544-551
Prediction of Dispersive Errors in Numerical Solution of the Euler Equations....Pages 552-561
Numerical Prediction of Shock Wave Focusing Phenomena in Air with Experimental Verification....Pages 562-573
Fundamental Aspects of Numerical Methods for the Propagation of Multi-Dimensional Nonlinear Waves in Solids....Pages 574-588
On a Nonlinear Telegraph Equation with a Free Boundary....Pages 589-598
“TVD” Schemes for Inhomogeneous Conservation Laws....Pages 599-607
The L1-Norm Distinguishes the Strictly Hyperbolic from a Non-Strictly Hyperbolic Theory of the Initial Value Problem For Systems of Conservation Laws....Pages 608-616
The Riemann Problem with Umbilic Lines for Wave Propagation in Isotropic Elastic Solids....Pages 617-629
Random-Choice Based Hybrid Methods for One and Two Dimensional Gas Dynamics....Pages 630-639
Some Features of Numerical Algorithms for Supersonic Flow Computation around Wings of Lifting Vehicles....Pages 640-647
A Fully Implicit High-Resolution Scheme for Chemically Reacting Compressible Flows....Pages 648-659
Stability of Semi-Discrete Approximations for Hyperbolic Initial-Boundary-Value Problems: Stationary Modes....Pages 660-670
Some Supraconvergent Schemes for Hyperbolic Equations on Irregular Grids....Pages 671-677
The Homogeneous Homentropic Compression or Expansion-A Test Case for Analyzing Sod’s Operator-Splitting....Pages 678-687
Global Existence of Solutions of Noncharacteristic Mixed Problems to Nonlinear Symmetric Dissipative Systems of the First Order....Pages 688-697
Stability of Initial Boundary Value Problems for Hyperbolic Systems....Pages 698-707
Back Matter....Pages 708-718

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Content:
Front Matter....Pages I-X
Non-Oscillatory Schemes for Multidimensional Euler Calculations with Unstructured Grids....Pages 1-10
Finite-Difference Schemes with Dissipation Control Joined to a Generalization of Van Leer Flux Splitting....Pages 11-20
Computation of Inviscid Vortical Flows in Piston Engines....Pages 21-30
Convexity in Hyperbolic Problems. Application to a Discontinuous Galerkin Method for the Resolution of the Polydimensional Euler Equations....Pages 31-42
Admissibility Conditions for Weak Solutions of Nonstrictly Hyperbolic Systems....Pages 43-50
Uniformly Second Order Convergent Schemes for Hyperbolic Conservation Laws Including Leonard’s Approach....Pages 51-62
High Resolution Finite Volume Schemes and Computational Aerodynamics....Pages 63-74
A Stability Analysis of a Eulerian Method for Some Surface Gravity Wave Problems....Pages 75-84
A Quadrature Approximation of the Boltzmann Collision Operator in Axisymmetric Geometry and Its Application to Particle Methods....Pages 85-95
Boundary Conditions for Nonlinear Hyperbolic Systems of Conservation Laws....Pages 96-104
Time-Marching Method to Solve Steady Incompressible Navier-Stokes Equations for Laminar and Turbulent Flow....Pages 105-114
On the Finite Velocity of Wave Motion Modelled by Nonlinear Evolution Equations....Pages 115-127
Hyperbolic Schemes for Multi-Component Euler Equations....Pages 128-138
Multigrid Methods for the Solution of Porous Media Multiphase Flow Equations....Pages 139-148
A standard model of generic rotational degeneracy....Pages 149-158
A Numerical Method for a System of Equations Modelling one-Dimensional three-Phase Flow in a Porous Medium....Pages 159-168
Nonuniqueness of Solutions for Riemann Problems....Pages 169-178
Simple Stability Criteria for Difference Approximations of Hyperbolic Initial-Boundary Value Problems....Pages 179-185
Hyperbolic Heat Transfer Problems with Phase Transitions....Pages 186-192
Unsymmetric Hyperbolic Systems and Almost Incompressible Flow....Pages 193-208
Frequency Decomposition Multi-Grid Methods for Hyperbolic Problems....Pages 209-217
Existence and Uniqueness for Linear Hyperbolic Systems with Unbounded Coefficients....Pages 218-219
A Numerical Method for Computing Viscous Shock Layers....Pages 220-229
Solution of the Euler Equations for Unsteady, Two-Dimensional, Transonic Flow....Pages 230-237
On some Recent Results for an Explicit Conservation Law of Mixed Type in One Dimension....Pages 238-245
Qualitative behavior of solutions for Riemann problems of conservation laws of mixed type....Pages 246-256
Strongly Nonlinear Hyperbolic Waves....Pages 257-268
The Structure of the Riemann Solution for Non-Strictly Hyperbolic Conservation Laws....Pages 269-278
Detonation Initiation Due to Shock Wave-Boundary Interactions....Pages 279-288
Nonconvex Scalar Conservation Laws in One and Two Space Dimensions....Pages 289-299
Upwind Schemes for the Navier-Stokes Equations....Pages 300-309
Normal Reflection Transmission of Shocks Waves on a Plane Interface between Two Rubber-Like Media....Pages 310-319
On the Concept of Weak Solutions in the BV-Space....Pages 320-328
Numerical Solution of the Euler Equations Used for Simulation of 2D and 3D Steady Transonic Flows....Pages 329-341
Numerical schemes for the Euler equations in two space dimensions without dimensional splitting....Pages 342-352
Initial-Boundary Value Problems for Transonic Equations in the Unbounded Domain....Pages 353-361
Entropy Weak Solutions to Nonlinear Hyperbolic Systems in Nonconservation Form....Pages 362-373
A Velocity-Pressure Model for Elastodynamics....Pages 374-383
Higher Order Accurate Kinetic Flux Vector Splitting Method for Euler Equations....Pages 384-392
Monte Carlo Finite Difference Methods for the Solution of Hyperbolic Equations....Pages 393-402
Numerical Solution of Flow Equations an Aircraft Designer’s View....Pages 403-412
Hypersonic Blunt Body Computations Including Real Gas Effects....Pages 413-422
Airfoil Calculations in Cartesian Grids....Pages 423-434
Characteristic Galerkin Methods for Hyperbolic Systems....Pages 435-455
Numerical Simulations of Compressible Hydrodynamic Instabiltities with High Resolution Schemes....Pages 456-465
On the “Flux-Difference Splitting” Formulation....Pages 466-481
On Overdetermined Hyperbolic Systems....Pages 482-488
Runge-Kutta Split-Matrix Method for the Simulation of Real Gas Hypersonic Flows....Pages 489-498
On Some Viscoelastic Strongly Damped Nonlinear Wave Equations....Pages 499-509
TVD Schemes to Compute Compressible Viscous Flows on Unstructured Meshes....Pages 510-520
Nonstationary Shock Wave Generation in Droplet Vapour Mixtures....Pages 521-529
Nonlinear Resonance Phenomena for the Euler — Equations Coupled with Chemical Reaction — Kinetics....Pages 530-543
The Design of Algorithms for Hypersurfaces Mowing with Curvature-Dependent Speed....Pages 544-551
Prediction of Dispersive Errors in Numerical Solution of the Euler Equations....Pages 552-561
Numerical Prediction of Shock Wave Focusing Phenomena in Air with Experimental Verification....Pages 562-573
Fundamental Aspects of Numerical Methods for the Propagation of Multi-Dimensional Nonlinear Waves in Solids....Pages 574-588
On a Nonlinear Telegraph Equation with a Free Boundary....Pages 589-598
“TVD” Schemes for Inhomogeneous Conservation Laws....Pages 599-607
The L1-Norm Distinguishes the Strictly Hyperbolic from a Non-Strictly Hyperbolic Theory of the Initial Value Problem For Systems of Conservation Laws....Pages 608-616
The Riemann Problem with Umbilic Lines for Wave Propagation in Isotropic Elastic Solids....Pages 617-629
Random-Choice Based Hybrid Methods for One and Two Dimensional Gas Dynamics....Pages 630-639
Some Features of Numerical Algorithms for Supersonic Flow Computation around Wings of Lifting Vehicles....Pages 640-647
A Fully Implicit High-Resolution Scheme for Chemically Reacting Compressible Flows....Pages 648-659
Stability of Semi-Discrete Approximations for Hyperbolic Initial-Boundary-Value Problems: Stationary Modes....Pages 660-670
Some Supraconvergent Schemes for Hyperbolic Equations on Irregular Grids....Pages 671-677
The Homogeneous Homentropic Compression or Expansion-A Test Case for Analyzing Sod’s Operator-Splitting....Pages 678-687
Global Existence of Solutions of Noncharacteristic Mixed Problems to Nonlinear Symmetric Dissipative Systems of the First Order....Pages 688-697
Stability of Initial Boundary Value Problems for Hyperbolic Systems....Pages 698-707
Back Matter....Pages 708-718
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