Linear Interpolation Between AMR Levels

[Abisleiman]

Does linear interpolation between AMR levels exist as a feature in AMReX? When a cell is refined it uses a piecewise constant interpolation to the new level currently. Is there a way to use a linear interpolation to the newly created level upon refinement. Piecewise constant interpolation is a limiting factor in increasing AMR levels where differing gradients are used to tag or when a large increase in AMR level is desired. In this situation artificially steep gradients are created that lead to stability issues.

[WeiqunZhang]

When a cell is refined it uses a piecewise constant interpolation to the new level currently.

Not sure what you mean. AMReX provides a number of interpolaters. It's up to the user which one to use. For example, these two tests both use cell_cons_interp, which is linear interpolation with limiting. (https://github.com/AMReX-Codes/amrex/blob/development/Src/AmrCore/AMReX_Interpolater.cpp#L37)

• https://github.com/AMReX-Codes/amrex/blob/development/Tests/Amr/Advection_AmrCore/Source/AmrCoreAdv.cpp#L457

• https://github.com/AMReX-Codes/amrex/blob/development/Tests/Amr/Advection_AmrLevel/Source/AmrLevelAdv.cpp#L132

[ZiyangHuang]

Hi Weiqun,

I check the link you gave (https://github.com/AMReX-Codes/amrex/blob/development/Src/AmrCore/AMReX_Interpolater.cpp#L37), and saw that CellConservativeLinear lincc_interp; and CellConservativeLinear cell_cons_interp(false);. It seems that lincc_interp is the one with limiting and cell_cons_interp is the one without. Moreover, what limter is applied in CellConservativeLinear, and is the limiter TVD?

Thanks!

[WeiqunZhang]

Both lincc_interp and cell_cons_interp do limiting. The difference is their approach for multiple variables. For cell_cons_interp, each variable is handled independently, whereas for lincc_interp all variables are limited by the same factor (that is their second-order centered difference slopes are reduced by the same factor). The limiter used in CellConservativeLinear is the the monotonized central limiter, which is second-order TVD.