Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Description

Transport by incompressible velocity fields is ubiquitous in applied mathematics and fluid dynamics. In practice, however, numerical discretization in time and space, as well as the use of approximate projection methods, can introduce spurious compression. These errors are often subtle, but when left unaddressed they accumulate over time and can significantly degrade the accuracy of advection schemes, distort transported quantities, and contaminate multiphase flow simulations.     In this talk, I will introduce the characteristic bending method, a general advection scheme for incompressible flows. The approach builds on semi-Lagrangian characteristic tracing and the reference map framework, and incorporates a volume-preserving projection that removes compressible errors introduced by numerical approximation. This projection can be interpreted as "bending" characteristics toward the divergence-free space, preserving mass and geometric structure of the advected fields. I will briefly review approximate projection methods for the incompressible Navier–Stokes equations and their extension to multiphase flows, then use canonical linear and nonlinear advection examples to demonstrate how characteristic bending filters spurious compression from the advecting velocity. I will conclude by showing how the method integrates into a multiphase solver and the resulting improvements in robustness and accuracy.