projects
From Geometry to Physics without Boundary-Fitted Meshing
This talk gives a brief overview of my work on non-boundary- and non-interface-fitted methods for multiphysics simulation on complex domains, focusing on the Shifted Boundary Method (SBM) and Shifted Interface Method (SIM). I discuss recent efforts to make these methods more accurate, efficient, and broadly applicable, including interface mechanics applications in solid mechanics and crystal plasticity.
Left ventricle simulations Using the Immersogeometric Analysis
This project focuses on simulating the left ventricle using immersogeometric analysis. I am responsible for generating volumetric meshes for the finite element method (FEM) from non-watertight surface meshes provided by UT Austin. In addition, I implemented the Fortran code that reads the displacement of the heart wall and the mitral valve, applying them as velocity boundary conditions for the fluid domain. The simulation follows a one-way coupling approach.
Pulsating Jet Simulations
Using the Proteus framework, I implemented custom boundary and initial conditions for pulsating jet simulations. These simulations were executed on the Frontera supercomputer, followed by postprocessing and visualization of the results.
Optimal Surrogate Boundary interactive
The Shifted Boundary Method (SBM) replaces the true geometry boundary integration (Γ) with a surrogate boundary integration (Γ̃) built from element edges, and uses a Taylor expansion to shift the boundary condition from Γ̃ back to Γ. The accuracy of SBM is governed by how close Γ̃ lies to Γ: the smaller the shift distance |d|, the smaller the consistency error.
A cell-inclusion parameter λ controls how the surrogate is constructed — only cells whose interior fraction is at least (1 − λ) are kept. λ = 0.5 minimizes the mean distance between Γ̃ and Γ, giving the best L2 accuracy. Drag the slider below to see how the surrogate boundary moves.
Exact analytical or CAD geometry.
Approximation built from element edges.
At λ = 0.5, the surrogate balances kept/discarded cells so the mean shift |d| — and therefore the L2 error — is minimised.
Highly Parallel Incompressible Flow Simulations Using the Shifted Boundary Method
This project focuses on simulating incompressible fluid flow over complex geometries using the Shifted Boundary Method, built on a highly parallel incomplete octree framework.
Efficient simulations based on Shifted Boundary Method and Adaptive Mesh Refinement
This project focuses on simulating fluid flow over complex geometries using the Shifted Boundary Method and dynamic adaptive octree meshes.
FlowBench: Incompressible Flow Simulations Dataset over Complex Geometries for SciML
This framework was used to generate simulations of flow past complex geometries and lid-driven cavity flow with obstacles for training scientific machine learning (SciML) models.
Flow past complex geometry (Argonne) using the Shifted Boundary Method.
Improved Convergence and User Experience of Welding Simulations
To enhance user-friendliness and improve the convergence of welding simulations, we introduced several key implementations:
- Central block-restrictable control
- Improved initial condition settings for newly activated elements via IC (Initial Condition) extrapolation using patch recovery
- A new Action enabling users to simulate the heated material addition process in welding simulations
In FY26, we extended libMesh projection APIs to support selected elements and variables (PR #4368), improving the reinitialization workflow of ElementSubdomainModifier.
Welding simulation without and with IC extrapolation -- left: without IC extrapolation; right: with IC extrapolation.