euler2d: 2-D inviscid flow/adjoint solver

euler2d is a 2-dimensional inviscid flow and adjoint solver. It solves the Euler equations of gas dynamics on unstructured triangular grids using a vertex-centroid scheme which is second order accurate. The adjoint solver is developed using the automatic differentiation tool Tapenade. Both the flow and adjoint solvers are accelerated using matrix-free LUSGS scheme.

A brief description of the algorithms used here is given in a [[http://euler2d.sourceforge.net/docs/nal-pd-cf-0604.pdf|technical report]].

=====Getting the code=====

You can get the source via anonymous svn by executing the following command

<code>

svn checkout http://euler2d.svn.sourceforge.net/svnroot/euler2d

</code>

This will create a directory called //euler2d// which contains all the sources. The sub-directories are

* //src-flo//: This contains the flow solver files.

* //src-adj//: This contains the adjoint solver files.

* //src-mesh//: This contains files for mesh deformation and mesh adjoint computation.

* //tapenade//: This contains some tapenade related files.

* //examples//: This contains some example grids and test cases.

You can also browse the source code in the [[http://euler2d.svn.sourceforge.net/viewvc/euler2d/|svn repository]].

=====Compiling the code=====

* The code is compiled using //make//. I have tested it only with GNU make.

* You will need a fortran and C compiler, and the AD tool //Tapenade// (for adjoint solver only, see below for link to Tapenade website).

* The Makefile assumes that you have already set a fortran compiler in the shell environment variable ''F77''. You can also set it in //Makefile.in// which is located in the base directory. Read the comments in this file.

* Note that gcc is required since I do some preprocessing of some fortran source files; you may be able to use other C compilers but I have not tested any.

* You can compile the flow, adjoint and mesh programs from the base directory or by going inside the corresponding directories. In the base directory, type ''make flo'' or ''make adj'' or ''make mesh'' to compile the individual programs. Type ''make'' to compile all of them.

* The executables are saved in the corresponding directories; you may want to set your ''PATH'' variable to include these directories or copy the executables to some other directory which is already in your path.

=====Limitations=====

This is not an exhaustive list of limitations.

* The flux function cannot be changed using the input files. By default, KFVS subroutines are called. If you want to use a different flux function, you have to make changes in all the required files.

* The limiter also cannot be controlled from the input files. You must edit the flux subroutines to switch on/off the limiter.

* Only two boundary types are supported, solid wall and far-field. For far-field, Steger-Warming splitting combined with point vortex correction is used.

* For adjoint solver, the cost function is the lift coefficient. To use your own cost function, see the following files to get an idea of how to modify them.

* src-adj/cost_x.F

* src-adj/cost_q.F

* src-adj/costfunc.F

=====Input files=====

The input file for the flow solver should be of the following form:

Start 1

FlowType 1

Mach 0.40

AOA 0.00

Reynolds 100.0

CFL 1000.0

Explicit 0

LastIter 0

MaxIter 10000

MinRes 1.0e-6

SaveInt 100

NoIso 30

Flux 3

Limiter 0

FarBC 1 0.25 0.0

GridFile "./naca3.struct"

</code>

The adjoint solver requires both the flow input file and an extra input file which is of the following form:

Start 1

CFL 1000.0

Explicit 0

MaxIter 75000

MinRes 1.0e-6

SaveInt 100

NoIso 50

Flux 3

</code>

A brief description of the various parameters is given in the table.

^ Variable ^ Description ^

| Start | 1=Start from free stream conditions, 2=Start from previously saved solution|

| FlowType | Ignore this, not required |

| Mach | Mach number |

| AOA | Angle of attack in degrees |

| Reynolds | Ignore this, not required |

| CFL | CFL condition for time-step |

| Explicit | 1=Explicit, 0=Implicit |

| LastIter | Usefull for grid adaptation, otherwise set to 0|

| MaxIter | Maximum number of time steps |

| MinRes | Residue for determining convergence |

| SaveInt | Interval at which results will be saved |

| NoIso | Number of iso-contours for gnuplot visualization |

| Flux | Numerical flux function (not implemented yet) |

=====Running and visualizing output=====

Try the example test cases given in the //examples// directory. First run the flow solver:

<code>

$ flo flo.inp

</code>

and then if you want, you can run the adjoint solver

<code>

$ adj flo.inp adj.inp

</code>

A lot of data is generated as output. The geometry and the grid are saved in BD.DAT and GRID.DAT which can be visualized using gnuplot:

<code>

gnuplot> set size square

gnuplot> plot 'BD.DAT' w l,'GRID.DAT' w l

</code>

The flow/adjoint solution is saved in three different formats. These files are written by src-flo/results.f and src-adj/results.f files.

* gnuplot: FLO.M, FLO.P, FLO.VECT, ADJ.D, ADJ.U, ADJ.V, ADJ.E, ADJ.VECT

* vigie: FLO.VIG, ADJ.VIG

* vtk: FLO.VTK, ADJ.VTK

* residue information: FLO.RES, ADJ.RES

* general files: FLO.DAT, ADJ.DAT

=====Links=====

* [[http://www-sop.inria.fr/tropics|Tapenade]]: Automatic differentiation tool.

* [[http://gnuplot.info|Gnuplot]]: GNU scientific data visualization program.

* [[http://www-sop.inria.fr/sinus/softs/vigie.html|Vigie]]: A nice visualization tool for 2-D and 3-D data.

* [[http://mayavi.sourceforge.net|MayaVi]]: A VTK-based visualization tool.

* [[http://www-rocq1.inria.fr/gamma/cdrom/www/bamg/eng.htm|BAMG]]: 2-D anisotropic grid generation program.

* [[http://www.cerfacs.fr/~muller/delaundo.html|Delaundo]]: 2-D grid generation program, mainly for isotropic grids.

* [[http://www.trilon.com/xv/xv.html|XV]]: A nice image viewer.

<note>

I am not actively working on this code at present. However you are welcome to write to me if you have any questions.

</note>

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