Proposal: extend Richardson convergence harness to support N-dimensional refinement

[AstroKriel]

The Richardson convergence harness (src/util/richardson.hpp) currently refines only in x, with ny/nz fixed at 8 cells per problem. This is correct for grid-aligned wave tests, but means oblique waves cannot be convergence-tested: transverse resolution is never refined, so errors plateau rather than converge.

Proposed change

Add setup.refine_n_dims (default: 1) to the harness Parameters struct. The harness computes ny and nz as:

• refine_n_dims = 1: ny = 8, nz = 8 (current behaviour; default)
• refine_n_dims = 2: ny = nx, nz = 8
• refine_n_dims = 3: ny = nx, nz = nx

The runTest callable signature changes from runTest(int nx) to runTest(int nx, int ny, int nz). Each problem lambda uses all three values when setting amr.n_cell.

CI impact

None. The default (refine_n_dims = 1) is identical to current behaviour. Higher-dimensional refinement is opt-in via TOML.

Motivation

Two motivations:

Immediate: combining correctness and convergence tests into a single binary (see #1916) creates a param conflict. The convergence harness forces ny = nz = 8 regardless of the wave physics, while the sim mode may run on a 3D domain. Adding refine_n_dims gives the convergence infrastructure an explicit notion of domain dimensionality so both modes are consistent.

Longer term: enables proper convergence testing for oblique wave propagation (modes in y/z), and makes the harness more generally useful for future problems that need multi-dimensional refinement.

Relation to other proposals

Dependency of #1916, which consolidates wave correctness and convergence tests. num_modes_y and num_modes_z are deferred until this extension lands.

[chongchonghe]

i suggest another design of multi-dim refinement: define nx_min nx_max ny_min ny_max nx_min nz_max, all default to 8. a pair at a direction like (nx_min, ny_min) can be either identical, or different by N fold (power 2). If there are multiple dimensions with N > 0, then they should all be identical; in this way you double multiple dimensions simultaneously.

[AstroKriel]

i suggest another design of multi-dim refinement: define nx_min nx_max ny_min ny_max nx_min nz_max, all default to 8. a pair at a direction like (nx_min, ny_min) can be either identical, or different by N fold (power 2). If there are multiple dimensions with N > 0, then they should all be identical; in this way you double multiple dimensions simultaneously.

Thanks for the suggestion!

My only concern is that the extra degrees of freedom that your suggestion introduces makes this harder to implement and opens the door to a few ill-defined configurations. For example, a user could set ny_min = 16, ny_max = 128 while leaving nx_min = nx_max = 8 (fixed), refining only in y. Whether that is physically meaningful depends entirely on the wave direction, and the test infrastructure has no way to detect a misconfiguration. Your constraint that all refined dimensions must cover the same range helps, but it still has to be checked and enforced explicitly, which adds complexity to both the harness and each problem's runTest lambda.

The refine_n_dims design was intentional on this point: by tying ny and nz to nx directly (ny = nx for refine_n_dims >= 2), the Richardson infrastructure guarantees cubic refinement automatically, the dx = 1/nx convergence rate computation stays unambiguous, and there are no extra parameters for a user to misconfigure.

Is there a specific use case or reason that motivated your suggestion? If there is a need for non-cubic or asymmetric refinement ranges, I'd be happy to explore changes to the proposal.

[chongchonghe]

I think your plan is fine, as long as you accept that the elongated directions can only be:

1. X
2. X and Y
3. X, Y, and Z
   and the fixed dimensions always have 8 grids.

I think this is a reasonable choice because you can always rotate your problem so that it aligns this way. So I agree, your plan is good.

[AstroKriel]

I think your plan is fine, as long as you accept that the elongated directions can only be:

1. X
2. X and Y
3. X, Y, and Z
   and the fixed dimensions always have 8 grids.

I think this is a reasonable choice because you can always rotate your problem so that it aligns this way. So I agree, your plan is good.

Great, I'll keep you posted!

[AstroKriel]

Closed by #1978