[t.oliveira]

Dear Foamers,

OpenFOAM offers schemes for strictly bounded versions "for the following schemes: limitedLinear, vanLeer, Gamma, limitedCubic, MUSCL", that is, one can use limitedLimitedLinear, limitedVanLeer, limitedGamma, limitedLimitedCubic, limitedMUSCL.

However, aren't the schemes vanLeer, Gamma, limitedCubic and MUSCL already bounded themselves (and limitedLinear if used with coefficient 1), because they are TVD?

Could you please tell me if I am missing something here?

Best regards,
Thomas Oliveira

Supporting info:
Gamma
"High resolution NVD differencing scheme for arbitrarily unstructured meshes". H Jasak, HG Weller, AD Gosman. International journal for numerical methods in fluids 31 (2), 431-449

limitedCubic
Comment "// Limit the limiter to obey the TVD constraint" in src/finiteVolume/interpolation/surfaceInterpolation/limitedSchemes/limitedCubic/limitedCubic.H

limitedLinear 1
return max(min(twoByk_*r, 1), 0); // in src/finiteVolume/interpolation/surfaceInterpolation/limitedSchemes/limitedLinear/limitedLinear.H

MUSCL
return max(min(min(2*r, 0.5*r + 0.5), 2), 0); // in src/finiteVolume/interpolation/surfaceInterpolation/limitedSchemes/MUSCL/MUSCL.H

vanLeer
return (r + mag(r))/(1 + mag(r)); // in src/finiteVolume/interpolation/surfaceInterpolation/limitedSchemes/vanLeer/vanLeer.H

[dybuk]

These schemes are not olny TVD but also you can specify a physical bounds for values.
For example " limitedLimitedLinear -2 2 1 " corresponds to limitedLinear scheme with coefficient 1 that bound field values between -2 and 2.

[t.oliveira]

Thank you, dybuk.

If I am solving an advection-diffusion problem, the boundary conditions are already within the physical bounds, and the discretization scheme for the convective term is TVD, isn't the solution already guaranteed to be within the physical bounds, without needing to use one of the limited versions of the TVD schemes?

Best regards,
Thomas Oliveira