You’d be more likely to get some kind of waves that propagate at fixed speed along the grid, giving you a privileged rest frame, like in the old discredited theories of aether.

I’ll try to steelman Florian_Dietz.

I don’t know much anything about relativity, but waves on a grid in computational fluid dynamics (CFD for short) typically don’t have the problem you describe. I do vaguely recall some strange methods that do in a Lagrangian CFD class I took, but they are definitely non-standard and I think were used merely as simple illustrations of a class of methods.

Plus, some CFD methods like the numerical method of characteristics discretize in different coordinates that follow the waves. This can resolve waves really well, but it’s confusing to set up in higher dimensions.

CFD methods are just particularly well developed numerical methods for physics. From what I understand analogous methods are used for computational physics in other domains (even relativity).

I don’t know much anything about relativity, but waves on a grid in computational fluid dynamics (CFD for short) typically don’t have the problem you describe.

Not even for wavelengths not much longer than the grid spacing?

I don’t see how that would be a problem. Perhaps I’m missing something, so if you could explain I’d be appreciative.

Usually the problem is that wavelengths smaller than the grid size obviously can’t be resolved. A class of turbulence modeling approaches can help with that to a certain extent. This class of methods is called “large eddy simulation”, or LES for short. You apply a low pass filter to the governing equations and then develop models for “unclosed” terms. In practice this is typically done less rigorously than I’d like, but it’s a valid modeling approach in general that should see more use in other fields. (Turbulence modeling is an interesting field in itself that a rational person might be interested in studying simply for the intellectual challenge.)

I’ll try to steelman Florian_Dietz.

I don’t know much anything about relativity, but waves on a grid in computational fluid dynamics (CFD for short) typically don’t have the problem you describe. I do vaguely recall some strange methods that do in a Lagrangian CFD class I took, but they are definitely non-standard and I think were used merely as simple illustrations of a class of methods.

Plus, some CFD methods like the numerical method of characteristics discretize in different coordinates that follow the waves. This can resolve waves really well, but it’s confusing to set up in higher dimensions.

CFD methods are just particularly well developed numerical methods for physics. From what I understand analogous methods are used for computational physics in other domains (even relativity).

Not even for wavelengths not much longer than the grid spacing?

I don’t see how that would be a problem. Perhaps I’m missing something, so if you could explain I’d be appreciative.

Usually the problem is that wavelengths smaller than the grid size obviously can’t be resolved. A class of turbulence modeling approaches can help with that to a certain extent. This class of methods is called “large eddy simulation”, or LES for short. You apply a low pass filter to the governing equations and then develop models for “unclosed” terms. In practice this is typically done less rigorously than I’d like, but it’s a valid modeling approach in general that should see more use in other fields. (Turbulence modeling is an interesting field in itself that a rational person might be interested in studying simply for the intellectual challenge.)