Godunov Methods: Theory and Applications

Front Matter....Pages i-xvii
OleĬnik’s E-Condition from the Viewpoint of Numerics....Pages 1-25
New Results for Residual Distribution Schemes....Pages 27-43
Simulations of Relativistic Jets with Genesis....Pages 45-52
Relativistic Jets from Collapsars....Pages 53-59
Exact Computation in Numerical Linear Algebra: The Discrete Fourier Transform....Pages 61-67
Comparative Study of HLL, HLLC and Hybrid Riemann Solvers in Unsteady Compressible Flows....Pages 69-75
A New Reconstruction Technique for the Euler Equations of Gas Dynamics with Source Terms....Pages 77-88
Colella-Glaz Splitting Scheme for Thermally Perfect Gases....Pages 89-95
Meshless Particle Methods: Recent Developments for Nonlinear Conservation Laws in Bounded Domain....Pages 97-108
Application of Wave-Propagation Algorithm to Two-Dimensional Thermoelastic Wave Propagation in Inhomogeneous Media....Pages 109-116
Unstructured Mesh Solvers for Hyperbolic PDES with Source Terms: Error Estimates and Mesh Quality....Pages 117-123
Constancy Preserving, Conservative Methods for Free-Surface Models....Pages 125-133
Hyperbolic-Elliptic Splitting for the Pseudo-Compressible Euler Equations....Pages 135-140
Godunov Solution of Shallow Water Equations on Curvilinear and Quadtree Grids....Pages 141-148
A Higher-Order-Accurate Reconstruction for the Computation of Compressible Flows on Cell-Vertex Triangular Grids....Pages 149-154
Numerical Experiments with Multilevel Schemes for Conservation Laws....Pages 155-160
Volume-of-Fluid Methods for Partial Differential Equations....Pages 161-177
Some New Godunov and Relaxation Methods for Two-Phase Flow Problems....Pages 179-188
Development of Genuinely Multidimensional Upwind Residual Distribution Schemes for the System of Eight Wave Ideal Magnetohydro-Dynamic Equations on Unstructured Grids....Pages 189-196
Application of TVD High Resolution Schemes to the Viscous Shock Tube Problem....Pages 197-202
Comparison of Numerical Solvers with Godunov Scheme for Multicomponent Turbulent Flows....Pages 203-208
Godunov-Type Schemes for the MHD Equations....Pages 209-216
Absorbing Boundary Conditions for Astrophysical MHD Simulations....Pages 217-224
About Kinetic Schemes Built in Axisymmetrical and Spherical Geometries....Pages 225-232
Lagrangian Systems of Conservation Laws and Approximate Riemann Solvers....Pages 233-245
Intermediate Shocks in 3D MHD Bow Shock Flows....Pages 247-252
A Second Order Godunov-Type Scheme for Naval Hydrodynamics....Pages 253-261
Uniformly High Order Methods for Unsteady Incompressible Flows....Pages 263-283
Application of the Finite Volume Method with Osher Scheme & Split Technique for Different Types of Flow in a Channel....Pages 285-291
A-Priori Estimates for a Semi-Lagrangian Scheme for the Wave Equation....Pages 293-300
Interstellar Shock Structures in Weakly Ionised Gases....Pages 301-307
The Ghost Fluid Method for Numerical Treatment of Discontinuities and Interfaces....Pages 309-317
A Hybrid Primitive-Conservative Upwind Scheme for the Drift Flux Model....Pages 319-326
Numerical Simulations of Relativistic Wind Accretion onto Black Holes Using Godunov-Type Methods....Pages 327-333
A Second Order Accurate, Space-Time Limited, BDF Scheme for the Linear Advection Equation....Pages 335-342
Multidimensional Upwind Schemes: Application to Hydraulics....Pages 343-365
Helmit — A New Interface Reconstruction Algorithm....Pages 367-376
A Godunov-Type Method for Studying the Linearised Stability of a Flow. Application to the Richtmyer-Meshkov Instability....Pages 377-397
Thermodynamics, Conservation Laws and their Rotation Invariance....Pages 399-410
A New Limiter that Improves TVD-MUSCL Schemes....Pages 411-417
Exact Roe Linearization for van der Waals’ Gas....Pages 419-424
The Godunov-Ryabenkii Condition: The Beginning of a New Stability Theory....Pages 425-443
A Front Tracking Method for Hybrid Grids....Pages 445-452
A Problem of Classical Shock Capturing Finite Volume Schemes in Hypersonic Flows....Pages 453-459
Orientation Effects on Bent Extragalactic Jets....Pages 461-467
Operator Splitting for Convection-Dominated Nonlinear Partial Differential Equations....Pages 469-475
Balancing Source Terms and Flux Gradients in Finite Volume Schemes....Pages 477-483
Riemann Solvers in General Relativistic Hydrodynamics....Pages 485-496
A Fully Adaptive Multiresolution Scheme for Shock Computations....Pages 497-503
Application of a Godunov-Type ALE-Method to Underwater Shock Waves....Pages 505-511
Numerical Simulation of 2-D Two-Phase Flows with Interface....Pages 513-518
Relativistic MHD Simulations Using a Godunov-type Method....Pages 519-526
Godunov Type Methods on Unstructured Grids and Local Mesh Refinement....Pages 527-547
3D Visualization of Shock Waves Using Volume Rendering....Pages 549-556
Gas Flows Generated by Propellant Burning....Pages 557-570
Finite Volume Evolution Galerkin Methods for Multidimensional Hyperbolic Systems....Pages 571-576
The Numerical Simulation of Relativistic Fluid Flow with Strong Shocks....Pages 577-594
An Artificial Compression Procedure Via Flux Correction....Pages 595-601
A Second Order Time-Splitting Technique for Advection-Dispersion Equation on Unstructured Grids....Pages 603-609
Towards Implicit Godunov Method: Exact Linearisation of the Numerical Flux....Pages 611-622
Mass Flux Computation as a Key to the Carbuncle Phenomenon....Pages 623-629
On the Positivity of FVS Schemes....Pages 631-637
The Carbuncle Phenomenon: A Genuine Euler Instability ?....Pages 639-645
A Godunov-type Solver for the Maxwell Equations with Divergence Cleaning....Pages 647-654
Convergence of Kinetic Approximation to Nonlinear Parabolic Problems....Pages 655-662
On Options for the Numerical Modelling of the Diffusion Term in River Pollution Simulations....Pages 663-670
Multidimensional Flux-Vector-Splitting and High-Resolution Characteristic Schemes....Pages 671-676
A Comparison of Roe, VFFC and AUSM+ Schemes for Two-Phase Water/Steam Flows....Pages 677-683
Low Dissipation Entropy Fix for Positivity Preserving Roe’s Scheme....Pages 685-690
Bicharacteristic Methods for Multi-Dimensional Hyperbolic Systems....Pages 691-698
An Exact Riemann Solver for Multidimensional Special Relativistic Hydrodynamics....Pages 699-705
Experience with the Osher Scheme for Applied Aerodynamics....Pages 707-715
A High-Resolution Godunov Method for Modeling Anomalous Fluid Behaviour....Pages 717-723
Toward Godunov-Type Methods for Hyperbolic Conservation Laws with Stiff Relaxation....Pages 725-744
Thermodynamics and Hyperbolic Systems of Balance Laws in Continuum Mechanics....Pages 745-761
Development and Application of High-Resolution Adaptive Numerical Techniques in Shock Wave Research Center....Pages 763-784
Interfaces, Detonation Waves, Cavitation and the Multiphase Godunov Method....Pages 785-807
One-Dimensional Calculation of Unsteady Open Channel Flow Using Adaptive Mesh Refinement....Pages 809-814
Error Estimates for Godunov-type Schemes in the Presence of Source Terms....Pages 815-821
A Multi-Dimensional Euler Solver....Pages 823-832
MPDATA-A Multipass Donor Cell Solver for Geophysical Flows....Pages 833-839
On the Hyperbolic Nature of Two-Phase Flow Equations: Characteristic Analysis and Related Numerical Methods....Pages 841-862
A Method of Lines Flux-Difference Splitting Finite Volume Approach for 1D and 2D River Flow Problems....Pages 863-871
A Simple Smoothing TVD Scheme on Structured and Unstructured Grids....Pages 873-878
Godunov Methods....Pages 879-898
Centred Unsplit Finite Volume Schemes for Multidimensional Hyperbolic Conservation Laws....Pages 899-906
Towards Very High Order Godunov Schemes....Pages 907-940
Model Hyperbolic Systems with Source Terms: Exact and Numerical Solutions....Pages 941-948
A Godunov-Type Method for Capturing Water Waves....Pages 949-968
A Staggered Scheme for Hyperbolic Conservation Laws Applied to Computation of Flow with Cavitation....Pages 969-976
An Expert System to Control the CFL Number of Implicit Upwind Methods....Pages 977-984
Discontinuous Galerkin Methods for Hyperbolic Partial Differential Equations....Pages 985-1005
Solving Incompressible Two-Phase Flows with a Coupled TVD Interface Tracking / Local Mesh Refinement Method....Pages 1007-1014
A Large Timestep Godunov-Type Model of Global Atmospheric Chemistry and Transport....Pages 1015-1022
Approximate Riemann Solvers, Godunov Schemes and Contact Discontinuities....Pages 1023-1056
A Unified Method for Compressible and Incompressible Flows with General Equation of State....Pages 1057-1064
Wave Interactions in Nonlinear Strings....Pages 1065-1071
Back Matter....Pages 1073-1077