SUPERCOMPUTING


Computational astrophysics and cosmology has advanced considerably in four decades, starting with simulations having only a few thousand particles or cells with just gravitational or hydrody- namic interactions to state-of-the-art simulations with hundreds of billions to trillions of resolution elements having several different types of interactions. To simulate the Universe with supercom- puters, we solve the nonlinear physics of gravity, fluid dynamics, and radiative transfer to model the evolution of dark matter, gas, and radiation. Physically-motivated models for the formation of stars, blackholes, and galaxies as well as supernova, active galactic nuclei, and radiative feedback also have to be included. I am currently developing and applying a meshfree finite-volume particle method (FVPM) hydro code for astrophysical and cosmological simulations.

TO MESH OR NOT TO MESH?


Computational fluid dynamics (CFD) is a powerful approach to solve the complex and nonlinear baryonic physics. Astrophysical and cosmological hydro codes are generally based on two main approaches: mesh-based finite-volume methods (FVM) and meshfree smoothed particle hydrodynamics (SPH). In FVM, space is discretized into non-overlapping cells using a mesh and the flux of mass, momentum, and total energy across cell faces are computed using well-developed solvers. This method has the advantage of being able to accurately capture shocks at high resolution, but the major disadvantage is that construction of a good mesh is technically difficult and computationally costly. In SPH, the fluid is discretized using particles, fluid variables are calculated by smoothing over neighbor particles using a weighted kernel function, and dynamical evolution equations are solved. This lagrangian approach has the major advantage of having high adaptivity and dynamic range, but disadvantages include requiring artificial viscosity and problems with mixing.

FINITE-VOLUME PARTICLE METHOD (FVPM)


FVPM (Hietel et al. 2000) was developed to self-consistently combine the best features of mesh-based and meshfree techniques. The fluid is discretized using particles which interact via their overlapping supports. When deriving the discrete conservation equations, unique integral definitions of the interaction vectors between neighboring particles are obtained. 1D and 2D tests show accurate results compared to FVM with unstructured meshes, but calculating the interaction vectors appears to be computationally infeasible in 3D. In the last few years, a new idea makes it possible to evaluate the particle interaction vectors exactly and relatively quickly (Quinlan & Nestor 2011). Thus, FVPM is now an advantageous and feasible approach for simulating hydrodynamics.

RADIATION-HYDRODYNAMICS


My RadHydro code combines N-body and hydrodynamic algorithms (Trac & Pen 2004) with an adaptive raytracing radiative transfer algorithm (Trac & Cen 2007) to directly and simultaneously solve collisionless dark matter dynamics, collisional gas dynamics, and radiative transfer of ionizing photons. This code has been used to run some of the largest and most detailed simulations of cosmic reionization, most recently with 30 billion dark matter particles, 30 billion gas cells, and 17 billion adaptive rays on Blacklight at the Pittsburgh Supercomputing Center (PSC).

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