How to implement higher-order coarse-to-fine interpolation with velocity gradients in AmrLevel?

[Afraid31]

Hi all,

I’m working on a 2D cell-centered flow solver using AMReX, and I’d like to perform higher-order coarse-to-fine interpolation of the velocity field between AMR levels.

Specifically, I want to reconstruct both velocity components using a quadratic polynomial form that includes both velocity values and their gradients from the coarse level:

This means the interpolation uses not only the cell-centered velocities on the coarse grid, but also the velocity gradients that are available at those cells.

I’m wondering:

What’s the best way to implement this kind of interpolation in the AMReX framework (within an AmrLevel class)?

Should I create a custom interpolation operator (e.g. a new InterpFaceRegister or InterpB variant), or is there an existing mechanism that supports high-order polynomial interpolation using gradient information?

[WeiqunZhang]

I think amrex::CellQuadratic does what you want. You just need to pass &amrex::quadratic_interp to FillPatch function.

See

amrex/Src/AmrCore/AMReX_MFInterp_2D_C.H

Line 490 in 546a888

void mf_cell_quadratic_calcslope (int i, int j, int /*k*/, int n,

and

amrex/Src/AmrCore/AMReX_MFInterp_2D_C.H

Line 526 in 546a888

fine(i,j,0,fcomp+n) = crse(ic,jc,0,ccomp+n)

[WeiqunZhang]

For AmrLevel based code, you tell it what intepolater to use in variableSetUp. For example,

amrex/Tests/Amr/Advection_AmrLevel/Source/AmrLevelAdv.cpp

Line 128 in 546a888

&cell_cons_interp);

And of course, you can also pass your custom interpolater.