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GAMMA = 1.4;
U = 3.0
V = 0.0 
RHO  = 1.4;

PRES = RHO*U*U/(GAMMA*MACH*MACH)
--PRES = 1;
--PRES = ./(MACH*RHO*RHO*GAMMA*GAMMA) 

SOUND = math.sqrt(U*U+V*V)/MACH

--[[ 
     Function for initial conditions
--]]
function free_stream( XYZ, FCT )
  for i=0,XYZ:size1()-1 do
    FCT:set(i,0,RHO) 
    FCT:set(i,1,RHO*U) 
    FCT:set(i,2,RHO*V) 
    FCT:set(i,3, 0.5*RHO*(U*U+V*V)+PRES/(RHO*GAMMA-1)) 
  end
end

--[[ 
     Example of a lua program driving the DG code
--]]
order = 1
print'*** Loading the mesh and the model ***'
myModel   = GModel  ()
myModel:load ('step.geo')
myModel:load ('step.msh')

print'*** Create a dg solver ***'
DG = dgSystemOfEquations (myModel)
DG:setOrder(order)
FS = functionLua(4, 'free_stream', {'XYZ'}):getName()

law=dgPerfectGasLaw2d()
DG:setConservationLaw(law)

law:addBoundaryCondition('Walls',law:newWallBoundary())
law:addBoundaryCondition('LeftRight',law:newOutsideValueBoundary(FS))

DG:setup()

print'*** setting the initial solution ***'

DG:L2Projection(FS)
DG:limitSolution()

print'*** export ***'

DG:exportSolution('output/solution_0')

print'*** solve ***'
CFL = 2.0;

for i=1,1000 do
    dt = CFL * DG:computeInvSpectralRadius();
    norm = DG:RK44_limiter(0.1*dt)
    print('*** ITER ***',i,dt, norm)
    if (i % 1 == 0) then 
       DG:exportSolution(string.format("output/solution-%06d", i)) 
    end
end

print'*** done ***'

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Added Navier Stokes & 2 test cases in DG
Added binary restart capabilities in DG
Added mesh renumbering option (-renumber)@

single file IO)

TWO BIG WARNINGS:

1) The MSH file version has been bumped from 2.1 to 2.2 because if a
mesh has partitions, the meaning of the tags has changed. Tag 3 used
to be the partition id; now tag 3 contains the number of partitions
(self+ghosts, if necessary), and the next tag(s) contain(s) the
partition(s) id(s). Ghost partitions have < 0 ids. The (new) default
behaviour is to not save partition numbers by default if there are
none.

2) There is an issue for split-file IO (one file per partition), due
to our on-the-fly renumbering of the elements (we would need a global
pass+store an inverse multimap to have the correct ghost element
numbers in a split-file scheme). The problem comes from the multiple
physicals -> multiple copies of the same MElement* in the MSH file +
our refusal to store an index in MElement. We need to discuss this
before we implement split-file IO in parallel...



PS -- I also changed the way we write binary files. We now save blobs
of single elements. This is fully compatible with old versions, but
might slow down reading large files. I did not see any performance hit
on my machine, but this should be tested more thoroughly. Third party
codes can still write larger binary blobs if they want to, but Gmsh
itself now writes small blobs, which makes the writeMSH routine much
simpler.

_storeVerticesInEntities.

Please SHOUT if you see something wrong when reading meshes: I'll revert the patch

Removes a bug occuring when matched edges aren't parametrized in the same direction as the original geometrical edge.

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though)

default after homology computatation for better generator chain visualization. 

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Changed homology generator chain mesh element orientations (determined by vertex order) so that
post-processing data isn't needed to save the generators, instead all the
elements have coefficient 1 now in the chain. Due to this also reverted
changes made to GModel writeMSH method in my earlier commit (they became obsolete).

entities.

Added option to save MSH without renumbering the mesh elements (required to
save post-processing $ElementData right!).