Irregular grid for finite differences PDE solution

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I got a project in a class I'm taking. In this project, I need to solve fluid dynamics and heat equations. Up to here, the problem is not so complicated, however the chamber shape is the problem: Chamber shape

as you can see, FE and JA makes this shape non rectangular. Since I want to keep the grid relatively simple, I though about creating a grid with "stairs" in those edges, that will look like that:

Stair approximation

I can quite easily calculate the area lost and use it as a measurement for the solution quality (let's say that I can allow 0.5% or less area loss).

Is it a good solution, or is there any better methods, assuming that I want to keep the grid relatively simple?

Thanks!