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Approach

Incompressible Navier-Stokes (INS) equations are a model for incompressible flows:


\begin{align} u_t + u \cdot \nabla u & = \nu \Delta u - \frac{1}{\rho} \nabla p \\ \nabla \cdot u & = 0 \end{align}


Chombo simulates incompressible flows using projection algorithms, which enforces the divergence-free constraint with the solution to an elliptic equation based on a Hodge Decomposition:


$v = u + \nabla \phi \quad \rightarrow \quad \nabla \cdot \nabla \phi = \nabla \cdot v$


This flexible approach has been extended to a number of other regimes, including Low-mach number and All-speed asymptotics of Compressible Navier Stokes with embedded boundaries..

Software

There are 3 software libraries that support INS:

In addition, we are currently working on a 4th-order accurate AMR INS solver on rectangular domains. For more details see the Current Research page.

Karman vortex street behind a cylinder at Re=300, using the EBAMRINS code. Different levels of refinement are used to minimize dissipation of the vortex street. See David Trebotich's page for a movie and more information.

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