CLAWPACK : EXEMPLES D'APPLICATION PROPOSES DANS LA LIBRAIRIE :
Ils sont contenus dans le repertoire clawpack/applications/
Subdirectories of claw/applications with a brief description of each problem
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advection
---------
claw/applications/advection/1d/inflow
1D advection equation with zero initial data and
sinusoidal boundary data at the left boundary.
claw/applications/advection/2d/const
2D advection equation with constant velocity (u,v) = (2,1),
periodic boundary conditions.
claw/applications/advection/2d/curvilinear/cylinder
2D advection equation solved on a polar coordinate grid.
The velocity field is potential flow around a cylinder
claw/applications/advection/2d/curvilinear/wiggly
2D advection equation with u = 0, v = 1 and
periodic boundary conditions solved on a wiggly nonorthogonal grid.
claw/applications/advection/2d/swirl
2D advection equation with swirling flow, taken from Example 9.6 in the
paper "High-resolution conservative algorithms for advection in
incompressible flow" [LeV95]
claw/applications/advection/2d/groundwater/copper95
2D advection equation with velocity field that was
generated by using Darcy's law with a discontinuous
permeability, as described in the paper [Ada95] listed in
claw/doc/biblio.ps.
------------
Burgers' eqn
------------
claw/applications/burgers/1d/sine2n/README
1D Burgers' equation with periodic boundary conditions and
sinusoidal initial data, which transforms into an N-wave.
claw/applications/burgers/2d/pwconst
2D Burgers' equation with piecewise constant initial data and
periodic boundary conditions.
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acoustics
---------
claw/applications/acoustics/1d/accuracy
Accuracy study for 1d acoustics equations.
claw/applications/acoustics/2d/constant/accuracy
Accuracy study for claw2 on 2d acoustics equations with radially symmetric
solution. "True solution" is obtained using claw1 with source terms.
claw/applications/acoustics/2d/constant/piston
3d acoustics, driven by a circular piston mounted on a wall.
Solved using claw2 with cylindrical symmetry about the x-axis.
claw/applications/acoustics/2d/varying/planewave
2d acoustics.
Plane wave hitting a discontinuity in sound speed.
claw/applications/acoustics/2d/varying/piston
3d acoustics, driven by a circular piston mounted on a wall,
in a tube with discontinuous wave speed at the boundary.
Solved using claw2 with cylindrical symmetry about the x-axis.
----------
Euler eqns
----------
claw/applications/euler/1d/pbc
1D Euler equations of gas dynamics with
piecewise constant initial data (the Riemann problem)
and periodic boundary conditions.
claw/applications/euler/1d/shocktube
1D Euler equations of gas dynamics with
piecewise constant initial data (the Riemann problem)
and extrapolation (outflow) boundary conditions.
claw/applications/euler/2d/accuracy
Accuracy study for claw2 on 2d Euler equations with radially symmetric
solution. "True solution" is obtained using claw1 with source terms.
claw/applications/euler/2d/radial
2D Euler equations of gas dynamics with piecewise constant initial data
having one value inside a circle and another value outside.
********************************************************************************************
**** Contenu du répertoire clawpack/applications/ :
-file pdes/claw/applications/README
+lib pdes/claw/applications/acoustics
for examples for linear acoustics
+lib pdes/claw/applications/euler
for examples for Euler equations of gas dynamics
+lib pdes/claw/applications/advection
for examples for linear advection equations
+lib pdes/claw/applications/burgers
for examples for Burgers' equation
********************************************************************************************
**** Contenu du répertoire clawpack/applications/acoustics :
+lib pdes/claw/applications/acoustics/1d
+lib pdes/claw/applications/acoustics/2d
******** Contenu du répertoire applications/acoustics/1d :
+lib pdes/claw/applications/acoustics/1d/accuracy
for accuracy study with constant coefficients
Accuracy study for 1d acoustics equations.
+lib pdes/claw/applications/acoustics/1d/rp
for Riemann solvers
-file pdes/claw/applications/acoustics/1d/rp/rp1ac.f
for Riemann solver for 1d acoustics with constant sound speed
-file pdes/claw/applications/acoustics/1d/rp/rp1acv.f
for Riemann solver for 1d acoustics with varying sound speed
-file pdes/claw/applications/acoustics/1d/rp/rp1acvc.f
for Varying sound speed -- using common blocks rather than aux array (old)
+lib pdes/claw/applications/acoustics/1d/varying
for varying sound speed.
1d acoustics equations with varying sound speed.
The example here is for a discontinuity in sound speed.
+lib pdes/claw/applications/acoustics/1d/varying.common
for varying sound speed using common block rather than aux,
from Version 2.0
1d acoustics equations with varying sound speed.
The example here is for a discontinuity in sound speed.
******** Contenu du répertoire applications/acoustics/2d :
+lib pdes/claw/applications/acoustics/2d/constant
+lib pdes/claw/applications/acoustics/2d/varying
+lib pdes/claw/applications/acoustics/2d/rp
************* Contenu du répertoire applications/acoustics/2d/constant :
+lib pdes/claw/applications/acoustics/2d/constant/accuracy
for example with 2d acoustics, radially symmetric, to check accuracy
Accuracy study for 2d acoustics equations.
This examples demonstrates a grid refinement study of the convergence rate.
claw2 is applied to the acoustics equations in 2 dimensions
with radially symmetric initial data consisting of a hump in pressure
and zero velocity. The pressure profile is specified in p0.f
The problem is also solved as a 1D problem using claw1
with a source term. The 1D problem is solved once on a fine grid and the 2D
problem is solved on one or more different grids. The error in the 1-norm
and max-norm are computed. Additional grids are obtained by halving the
mesh sizes dx, dy, and dt, and the results on successive grids are compared
to estimate the convergence rate (order of accuracy).
The solutions are also output in a form suitable for making contour plots of
the 2D solutions and also scatter plots of the 2D solutions in which q(x,y)
is plotted against r = sqrt(x^2 + y^2). This can be compared to the 1D
solution to see both how large the errors are and also how well the
multidimensional algorithm preserves radial symmetry.
+lib pdes/claw/applications/acoustics/2d/constant/piston
for example with cylindrical symmetry and circular piston mounted on wall
3d acoustics, driven by a circular piston mounted on a wall.
Solved using claw2 with cylindrical symmetry about the x-axis.
************* Contenu du répertoire applications/acoustics/2d/rp :
-file pdes/claw/applications/acoustics/2d/rp/rp2Aac.f
-file pdes/claw/applications/acoustics/2d/rp/rp2Bac.f
-file pdes/claw/applications/acoustics/2d/rp/rp2Aacv.f
-file pdes/claw/applications/acoustics/2d/rp/rp2Bacv.f
************* Contenu du répertoire applications/acoustics/2d/varying :
+lib pdes/claw/applications/acoustics/2d/varying/planewave
2d acoustics.
Plane wave hitting a discontinuity in sound speed.
+lib pdes/claw/applications/acoustics/2d/varying/piston
3d acoustics, driven by a circular piston mounted on a wall,
in a tube with discontinuous wave speed at the boundary.
Solved using claw2 with cylindrical symmetry about the x-axis.
********************************************************************************************
**** Contenu du répertoire clawpack/applications/advection :
+lib pdes/claw/applications/advection/2d
for examples of 2d advection
+lib pdes/claw/applications/advection/1d
for examples of 1d advection
******** Contenu du répertoire applications/advection/1d :
+lib pdes/claw/applications/advection/1d/rp
for Riemann solvers for 1d advection
+lib pdes/claw/applications/advection/1d/inflow
for 1d advection with constant velocity and inflow boundary data
1D advection equation with
zero initial data and
sinusoidal boundary data at the left boundary.
The computed solutions are written to fort.100, fort.101,...
The true solutions are written to fort.200, fort.201, ...
The errors in the solution are written to fort.errs and also to fort.terr
for an easy look at the error vs. time.
Second order accuracy should be observed if the grid is refined.
+lib pdes/claw/applications/advection/1d/varying
for 1d advection with varying velocity
************* Contenu du répertoire applications/advection/1d/rp :
-file pdes/claw/applications/advection/1d/rp/rp1ad.f
for Riemann solver for 1d advection q_t + u*q_x = 0 with u constant
-file pdes/claw/applications/advection/1d/rp/rp1ad1.f
for Riemann solver for 1d advection with u stored in aux, advective form
-file pdes/claw/applications/advection/1d/rp/rp1ad3.f
for Riemann solver for 1d advection with u stored in aux, conservative form
************* Contenu du répertoire applications/advection/1d/varying :
+lib pdes/claw/applications/advection/1d/varying/test1
for a(x) q_t + u0 * q_x = 0 using capacity function
+lib pdes/claw/applications/advection/1d/varying/test2
for q_t + u0/a(x) * q_x = 0 using variable velocity
******** Contenu du répertoire applications/advection/2d :
+lib pdes/claw/applications/advection/2d/const
2D advection equation with constant velocity (u,v) = (2,1),
specified in xvel.f and yvel.f.
Periodic boundary conditions.
+lib pdes/claw/applications/advection/2d/curvilinear
++lib pdes/claw/applications/advection/2d/curvilinear/cylinder
2D advection equation $q_t + (uq)_x + (vq)_y = 0$
solved on a polar coordinate grid using a grid transformation as
specified in setxpyp.f.
The velocity field is specified by xpvel.f and ypvel.f and gives
potential flow around a cylinder.
The initial data is a front moving in from the left.
A blob can be specified instead by changing a parameter in
the data file.
++lib pdes/claw/applications/advection/2d/curvilinear/wiggly
2D advection equation $q_t + (uq)_x + (vq)_y = 0$
with u = 0, v = 1 and
periodic boundary conditions
solved on a wiggly nonorthogonal grid.
Note advection is straight up, so the circular blob should remain circular.
The velocity is nonzero at the boundaries, so mass is not exactly conserved.
+lib pdes/claw/applications/advection/2d/swirl
2D advection equation $q_t + (uq)_x + (vq)_y = 0$ with swirling flow,
taken from Example 9.6 in the
paper "High-resolution conservative algorithms for advection in
incompressible flow",
+lib pdes/claw/applications/advection/2d/rp
-file pdes/claw/applications/advection/2d/rp/rpn2ad1.f
for normal Riemann solver for advection -- advective form, aux array
-file pdes/claw/applications/advection/2d/rp/rpn2ad2.f
for normal Riemann solver for advection -- advective form, xvel,yvel
-file pdes/claw/applications/advection/2d/rp/rpn2ad3.f
for normal Riemann solver for advection -- conservative form, aux array
-file pdes/claw/applications/advection/2d/rp/rpn2ad4.f
for normal Riemann solver for advection -- conservative form, xvel,yvel
-file pdes/claw/applications/advection/2d/rp/rpt2ad1.f
for transverse Riemann solver for advection -- aux array
-file pdes/claw/applications/advection/2d/rp/rpt2ad2.f
for transverse Riemann solver for advection -- xvel,yvel
+lib pdes/claw/applications/advection/2d/groundwater
++lib pdes/claw/applications/advection/2d/groundwater/copper95
2D advection equation $q_t + (uq)_x + (vq)_y = 0$ with
the velocity field specified by the data files ux.data and vy.data, which
give the data along the left and bottom edge of each cell respectively.
This data was generated by using Darcy's law with a discontinuous
permeability, and is described in the paper [Ada95] listed in
claw/doc/biblio.ps.
+lib pdes/claw/applications/advection/2d/stratified
2D advection equation with stratified flow,
rho(y)*q_t + u(x,y)*rho(y)*q_x + v(x,y)*rho(y)*q_y = 0
Three subdirectories contain code for three different grids:
cartesian
grid1
grid2
********************************************************************************************
**** Contenu du répertoire clawpack/applications/burgers :
+lib pdes/claw/applications/burgers/2d
for examples for Burgers' equation in 2d
+lib pdes/claw/applications/burgers/1d
for examples for Burgers' equation in 1d
******** Contenu du répertoire applications/burgers/1d :
+lib pdes/claw/applications/burgers/1d/sine2n
1D Burgers' equation with periodic boundary conditions and
sinusoidal initial data, which transforms into an N-wave.
+lib pdes/claw/applications/burgers/1d/rp
-file pdes/claw/applications/burgers/1d/rp/rp1bu.f
******** Contenu du répertoire applications/burgers/2d :
+lib pdes/claw/applications/burgers/2d/rp
for Riemann solvers for Burgers' equation
-file pdes/claw/applications/burgers/2d/rp/rp2Abu.f
-file pdes/claw/applications/burgers/2d/rp/rp2Bbu.f
+lib pdes/claw/applications/burgers/2d/pwconst
for example with piecewise constant initial data
2D Burgers' equation with
piecewise constant initial data and
periodic boundary conditions.
********************************************************************************************
**** Contenu du répertoire clawpack/applications/euler :
+lib pdes/claw/applications/euler/1d
for test problems for 1d Euler equations of gas dynamics
+lib pdes/claw/applications/euler/2d
for test problems for 2d Euler equations of gas dynamics
******** Contenu du répertoire applications/euler/1d :
+lib pdes/claw/applications/euler/1d/rp
-file pdes/claw/applications/euler/1d/rp/rp1eu.f
+lib pdes/claw/applications/euler/1d/pbc
1D Euler equations of gas dynamics with
piecewise constant initial data (the Riemann problem)
and periodic boundary conditions.
The data file is currently set for Sod's Riemann problem.
+lib pdes/claw/applications/euler/1d/shocktube
1D Euler equations of gas dynamics with
piecewise constant initial data (the Riemann problem)
and extrapolation (outflow) boundary conditions.
The data file is currently set for Sod's Riemann problem.
******** Contenu du répertoire applications/euler/2d :
+lib pdes/claw/applications/euler/2d/accuracy
for test problem computing 2d radially symmetric solutions vs. 1d solutions
Accuracy study for claw2 on 2d Euler equations with radially symmetric solution.
"True solution" is obtained using claw1 with source terms.
These examples demonstrate a grid refinement study of the convergence rate.
claw2 is applied to the Euler equations in 2 dimensions with radially symmetric
initial data consisting of a hump in density and energy (with constant
temperature) and zero velocity. The density profile is specified in rho.f
The problem is also solved as a 1D problem using claw1
with a source term. The 1D problem is solved once on a fine grid and the 2D
problem is solved on one or more different grids. The error in the 1-norm
and max-norm are computed. Additional grids are obtained by halving the
mesh sizes dx, dy, and dt, and the results on successive grids are compared
to estimate the convergence rate (order of accuracy).
The solutions are also output in a form suitable for making contour plots of
the 2D solutions and also scatter plots of the 2D solutions in which q(x,y)
is plotted against r = sqrt(x^2 + y^2). This can be compared to the 1D
solution to see both how large the errors are and also how well the
multidimensional algorithm preserves radial symmetry.
This program is quite complicated since both 1D and 2D problems are solved.
Moreover the 1D solutions must be passed to the 2D error calculation
routines in common blocks.
+lib pdes/claw/applications/euler/2d/quadrants
for 2d Riemann problem with data that is piecewise constant in quadrants
This directory contains an example driver routine for solving the 2D
Euler equations of gas dynamics with piecewise
constant initial data having 4 different values in 4 quadrants.
The particular problem is specified in the routine ic2rp2.f
+lib pdes/claw/applications/euler/2d/radial
for test problems with radially symmetric shocks
2D Euler equations of gas dynamics with piecewise constant initial data
having one value inside a circle and another value outside, as specified in
the data file.
The routine cellave in clawpack/claw2/misc is used to set the initial
conditions. This routine determines the fraction of the cell that lies on
each side on an initial discontinuity (as specified in fdisc.f).
+lib pdes/claw/applications/euler/2d/rp
for Riemann solvers for 2d Euler
-file pdes/claw/applications/euler/2d/rp/rpn2eu.f
for Roe solver for 2d Euler equations normal to interface
-file pdes/claw/applications/euler/2d/rp/rpt2eu.f
for transverse Riemann solver
********************************************************************************************