Ann S. Almgren

A cell-centered Cartesian grid projection method for the incompressible Euler equations in complex geometries

Many problems in fluid dynamics have domains with complicated internal or external boundaries of the flow. Here we present a method for calculating time-dependent incompressible inviscid flow using a Cartesian grid approach for representing geometry. In this approach, the body is represented as an interface embedded in a regular Cartesian mesh. The basic algorithm is a fractional-step projection method based on an approximate projection. The advection step is based on a Cartesian grid algorithm for compressible flow, in which the discretization of the body near the flow uses a volume-of-fluid representa-

Fates of the most massive primordial stars

We present our results of numerical simulations of the most massive primordial stars. For the extremely massive non-rotating Pop III stars over 300M⊙, they would simply die as black holes. But the Pop III stars with initial masses 140 - 260M⊙ may have died as gigantic explosions called pair-instability supernovae (PSNe). We use a new radiation-hydrodynamics code CASTRO to study evolution of PSNe. Our models follow the entire explosive burning and the explosion until the shock breaks out from the stellar surface. In our simulations, we find that fluid instabilities occurred during the explosion. These instabilities are driven by both nuclear burning and hydrodynamical instability. In the red supergiant models, fluid instabilities can lead to significant mixing of supernova ejecta and alter the observational signature.

On Using a Fast Multipole Method-based Poisson Solver in an Approximate Projection Method

Author(s): Williams, Sarah A.; Almgren, Ann S.; Puckett, E. Gerry | Abstract: Approximate projection methods are useful computational tools for solving the equations of time-dependent incompressible flow.In this report we will present a new discretization of the approximate projection in an approximate projection method. The discretizations of divergence and gradient will be identical to those in existing approximate projection methodology using cell-centered values of pressure; however, we will replace inversion of the five-point cell-centered discretization of the Laplacian operator by a Fast Multipole Method-based Poisson Solver (FMM-PS).We will show that the FMM-PS solver can be an accurate and robust component of an approximation projection method for constant density, inviscid, incompressible flow problems. Computational examples exhibiting second-order accuracy for smooth problems will be shown. The FMM-PS solver will be found to be more robust than inversion of the standard five-point cell-centered discretization of the Laplacian for certain time-dependent problems that challenge the robustness of the approximate projection methodology.