Modeling and Simulation Group Meeting (hidden)

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A two-point boundary value problem from ODEs with algebraic restrictions

Speaker: Vicente Gomez, Courant Institute

Location: Warren Weaver Hall 1302

Date: Thursday, December 7, 2023, 12:30 p.m.

Synopsis:

Describing incompressible fluids necessitates incorporating pressure, however, it is introduced in the equations with a lower differential order compared to velocity. This discrepancy complicates numerical schemes, often requiring additional boundary conditions or different discretization approaches for pressure and velocity.

 

In this talk we introduce a new formulation for the periodic channel, presenting an unexpectedly simple yet effective solution to resolve the mismatch between pressure and velocity in incompressible fluids. By employing this seemingly unconventional approach, we craft a well-conditioned system that successfully eliminates the traditional mismatch problem. Notably, this method's versatility extends beyond incompressible fluids, applicable to various differential-algebraic equations, such as inelastic fibers and curl-free fluids