Compressible Flow Simulation using FEniCS
I implemented a simulation of compressible fluid flow using the finite element framework FEniCS. The governing equations include the full NavierโStokes equations, accounting for variable density, momentum conservation, and thermal energy transport:
โข
Mass conservation: โฯ/โt + โยท(ฯu) = 0
โข
Momentum equation includes both viscous and pressure forces with variable density
โข
Energy conservation: accounts for heat convection and conduction
I derived and implemented the weak forms of these equations to suit finite element analysis.
During simulation, we encountered numerical instability, particularly in the advection term. To address this, we plan to incorporate SUPG (Streamline Upwind Petrov-Galerkin) stabilization, which mitigates oscillations and enhances robustness in advection-dominated flows.
This approach is expected to improve both convergence and physical realism of the compressible flow model.
