PACM Graduate Student Colloquium

Jonathan Palafoutas- PACM Graduate Student in his 4th year being advised by Romain Teyssier.

Title: Comparing a priori and a posteriori slope limiters for Euler’s equations 

Abstract: High-order numerical methods offer significant advantages over first- and second-order methods for certain hyperbolic PDEs, such as Euler’s equations for inviscid, compressible flow. For example, in very low–Mach-number problems, high-order methods often have lower overall computational cost than second-order methods; although they require more operations per element per time step, fewer elements are needed to achieve the same accuracy. However, high-order methods face challenges when capturing and robustly resolving strong shocks in high–Mach-number flows. Two main approaches are commonly used to limit slopes near discontinuities: (1) a priori limiters, which modify the numerical solution at time tⁿ⁺¹ using only information from time tⁿ, and (2) a posteriori limiters, which iteratively revise a candidate solution at time tⁿ⁺¹.In this work, I compare these two approaches for high-order finite-volume methods and examine their tradeoffs in accuracy, robustness, and computational cost. 

Tachin Ruangkriengsin- PACM Graduate Student in his 4th year being advised by Howard Stone.

Title: Transient rod climbing in a viscoelastic fluid

Abstract: The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the free surface rises along a rotating rod. Despite its striking appearance and long history, theoretical understanding of this phenomenon remains limited. In this talk, I will introduce the mechanics of viscoelastic fluids and show how asymptotic analysis in appropriate limits can be used to determine both the steady and transient interface heights in rod climbing. Comparisons with experimental measurements will also be presented.

Andy Zhang- PACM Graduate Student in his 4th year being advised by Amit Singer.

Title: Cryo-EM, Kam's Method, and the Method of Moments

Abstract: Kam’s method (proposed by Zvi Kam in 1970) is a statistical method-of-moments approach applied to the cryo-EM reconstruction problem that uses low-order moments of 2-D projection images taken uniformly over SO(3) to reconstruct a 3-D structure. A notable advantage to this method is its ability to bypass angular assignment, which is typically a large computational burden. In this talk, I will focus on an extension of Kam's method to nonuniform viewing angles, using it to solve for structures where a similar existing structure is known. If time allows, I will also discuss some of the challenges that arise when dealing with experimental cryo-EM images.