Embedded Boundary Methods for PDEs in Complex Geometries

Learn embedded boundary methods for solving partial differential equations in complex geometries through this 52-minute conference talk by Phillip Colella at IPAM's Boundary Conditions for Atomistic Simulations in Macroscopic Electrochemical Cells Workshop. Discover how irregular domains are represented computationally as collections of control volumes formed by intersecting rectangular Cartesian cells with the domain boundary. Explore the discretization process where PDEs in conservation form are integrated over control volumes with flux averages computed using quadratures on faces. Examine the construction of control volumes and associated geometric objects using implicit function representations of irregular domains. Understand the development of stable and accurate discretizations for classical PDEs, including high-order methods and adaptive mesh refinement techniques. See practical applications of these methods demonstrated through various examples including shocked flows, microfluidic flows, and surface diffusion problems.