# Physical System modeling and simulation using HPC

**Date:**

Computational Sciences has been at the forefront of Continuum Mechanics research for a long time. With the advent of cheaper and faster compute capability, it is not only possible to study aspects of a physical system where an experimental study might prove difficult, but also to numerically analyze problems with very high granularity. This talk showcased some of the work where High Performance Computing (HPC) was used by me to solve some of these problems - a Conjugate Gradient method based solver to solve systems of linear equations, which was used to solve Laplace Equation in a $1000 \times 1000$ grid (996004 unknowns) within $10^{-6}$ units of the analytical solution. A similar solver based on stabilized bi-conjugate gradient method was used to solve pressure Poisson equation in a level-set based immersed boundary method code to investigate how pitching and heaving affect the propulsion of a self-propelled oscillating airfoil. This study was used to shed some light on the hydrodynamics and flow structures during the transient state of fish like locomotion (the first few cycles during start of the motion). This task would have been especially difficult to simulate using an experimental setup.