To verify the second order accuracy of the 2DE-code the results of the computations of an established test-case of
Ma=0.63 flow for a NACA0012-airfoil at an angle of attach of 2 degrees are preseneted here. To demonstrate the
discretization dependant error reduction a set of three succesively refined grids are generated. Using a single block, structured euler o-grid
of 300x52 cells generated with UGRID the two coarser grids are created through
the omission of every other grid-line. For each of these grids 2DE is run using local time-stepping, a CFL number of 6.5, implicit residual smoothing
with variable coefficients scaled with an epsilon of 0.8, and 2nd and 4th order artificial viscosity terms scaled with factors of 0.5 and 1/64 respectively.
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A leading-edge detail of the o-grid series used for this verification is presented here. Black "x"s mark the nodes of the finest grid of
300x52 cells, red triangles those of the medium grid of 150x26 cells and finally blue circles the vertices of the coarsest grid made up of
75x13 cells. The creation of the coarser grids through successive removal of avery ohter grid line is clearly visible.
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The convergence plot for the three computations shows the expected more rapid decrease of the residual for the smaller grids. Full convergence
to machine accuracy was not attained for the finest grid, however the coefficients of lift and drag - plotted only for the finest grid here - reach
a constant value for all cases, allowing a valid statement for this accuracy verification.
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A plot of the surface mach number distribution for the three cases investigated show a significant difference betweeen the coarsest and the finest
grids, while the medium and fine grids differ only slightly. A detail of the suction peak is shown below.
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Detail of the mach number attained in the suction peak for the three cases shows that the offset to the grid independant solution decreases more than
linearly with a refinement of the grid, thus demonstarting the 2nd order accuracy of the code.
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Contour plot of the mach number in the vicinity of the airfoil shows the completely subsonic flow for this test case. And it's a pretty, colorful picture. :-)
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