Gallery of examples from the book FVMHP

Chapter 3: Characteristics and RiemannProblems for Linear Hyperbolic Equations.

$CLAW/book/chap3/acousimple ... README ... Plot Index

Acoustics example with data breaking into left and right-going waves, with solid wall at left and outflow at right.

Chapter 6: High-resolution methods

$CLAW/book/chap6/compareadv ... README ... Plot Index

Advection equation with first order upwind method. Periodic boundary conditions, looping around through unit period.

$CLAW/book/chap6/wavepacket ... README ... Plot Index

Advection equation with first order upwind method. Periodic boundary conditions, looping around through unit period.

Chapter 7: Boundary Conditions and Ghost Cells

$CLAW/book/chap7/advinflow ... README ... Plot Index

Advection equation with inflow boundary conditions.

$CLAW/book/chap7/acouinflow ... README ... Plot Index

Acoustics equations with inflow boundary condition.

$CLAW/book/chap7/standing ... README ... Plot Index

Acoustics eqautions with solid wall boundary conditions and a standing wave solution.

Chapter 9: Variable-Coefficient Linear Equations

$CLAW/book/chap9/acoustics/interface ... README ... Plot Index

Acoustics equations with variable coefficients and a single interface with no impedance jump.

$CLAW/book/chap9/acoustics/layered ... README ... Plot Index

Acoustics equations with variable coefficients in periodic layered medium.

Chapter 10: Other Approaches to High Resolution.

$CLAW/book/chap10/tvb ... README ... Plot Index

TVB method on the advection equation with wave-packet data and periodic boundary conditions.

Chapter 11: Nonlinear Scalar Conservation Laws.

$CLAW/book/chap11/burgers ... README ... Plot Index

Burgers' equation with oscillatory initial data to demonstrate decay to an N wave.

$CLAW/book/chap11/greenlight ... README ... Plot Index

Traffic flow equations. Riemann problem for cars starting at a green light.

$CLAW/book/chap11/redlight ... README ... Plot Index

Traffic flow equations. Riemann problem for cars stopping at a red light.

Chapter 12: Finite Volume Methods forNonlinear Scalar Conservation Laws.

$CLAW/book/chap12/efix ... README ... Plot Index

Burgers' equation with a transonic rarefaction wave. Comparison of results obtained with or without the entropy fix.

$CLAW/book/chap12/llf ... README ... Plot Index

Burgers' equation with a transonic rarefaction wave. Using the Local Lax-Friedrichs method.

$CLAW/book/chap12/nonconservative ... README ... Plot Index

Burgers' equation solved with a nonconservative upwind method, to demonstrate that this does not approximate the weak solution properly.

Chapter 13: Nonlinear Systems of Conservation Laws.

$CLAW/book/chap13/collide ... README ... Plot Index

1d Shallow water equations with initial data consisting of two 2-shocks, which collide and produce a 1-rarefaction and 2-shock.

Chapter 17: Source Terms and Balance Laws.

$CLAW/book/chap17/advdiff ... README ... Plot Index

Advection-diffusion equation solved with a fractional step method.

Chapter 20: Multidimensional Scalar Equations.

$CLAW/book/chap20/burgers ... README ... Plot Index

2D Burgers' equation at angle theta to the x-axis.

$CLAW/book/chap20/rotate ... README ... Plot Index

Advection equation for solid body rotation

Chapter 21: Multidimensional Systems.

$CLAW/book/chap21/radialdam ... README ... Plot Index

Radial dam-break problem for 2D shallow water equations.

Chapter 22: Elastic Waves.

$CLAW/book/chap22/corner ... README ... Plot Index

Elasticity equations in a region consisting of two materials with a corner.

Chapter 23: Finite Volume Methods on Quadrilateral Grids.

$CLAW/book/chap23/acoustics ... README ... Plot Index

2d acoustics with a radially-symmetric solution, solved on a skewed grid.