Navier-Stokes with Mimetic Methods

2D Lock exchange test case using mimetic methods
Updated 15 Feb 2021

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Single, extensively commented file that solves NS equations assuming small density and temperature variations (Boussinesq). I have opted for mimetic methods (via MOLE) and explicit forward time schemes. More elaborated and precise time discretization schemes contribute very little to this particular scenario. Numerical diffusion could be avoided by computing the transient terms using a symplectic method such as Leapfrog.

For sharp Kelvin-Helmholtz billows, use a dx == 0.0625, keep in mind the CFL condition imposed on dt for a two-dimensional advection problem. Picture was obtained using m = 1600, n = 320, and dt = 0.1

The most time-consuming part (as expected) is the computation of the pressure field, Laplacian matrix is highly sparse but not positive definite.

Cite As

Johnny Corbino Delgado (2024). Navier-Stokes with Mimetic Methods (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2020b
Compatible with R2018b and later releases
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

Just added a comment on stability, so the user knows how to set the time step based on spatial resolution given that only explicit schemes are employed.