Course Grader for M168 - Introduction to Finite Element Methods

- Lattice Boltzmann method is used to solve the two-dimensional incompressible viscous flow past an arbitrary body in a free flow or confined in a channel. Bhatnagar-Gross-Krook ( BGK ) operator is used as the linearized collision operator in the Boltzmann equation and recovers the Macroscopic Navier-Stokes Equation. - Single Relaxation Time ( SRT ) with a D2Q9 lattice model and a suitable equilibrium distribution function is used to "locally" and parallelly solve the Boltzmann equation across all the different lattice points. Bounce-Back and partial Bounce-Back schemes are used to implement no-slip and slip boundary conditions respectively. A first-order curved boundary treatment is used for complex geometries. - Momentum Exchange method is used to force evaluation ( drag and lift ). Bounce-back boundary conditions along with 1st-order interpolation of the post-collision distribution function at curved boundaries give fairly reliable force calculations for 2D flows.

Course Grader for M168 - Introduction to Finite Element Methods

Course Grader for MAE 156A - Advanced Strength of Materials

- Worked with Prof. Ratnesh Shukla from Mechanical Department. A large-scale, fully parallel two-dimensional solver is used to simulate the coupled interaction of rigid bodies moving in a viscous incompressible fluid. The solid boundary is described using a high-order level-set based description by the solver. This is combined with a simple Eulerian treatment of the fluid flow utilizing a staggered mesh and typical second-order central discretization.- Block structured Adaptive Mesh Refinement algorithm is used which tags the cells for refinement according to the vorticity value specified by the user. Appropriate formulation of ghost cells is done to capture the boundary. The ghost cells identified in the solid region are used to enforce the boundary conditions (no-penetration and no-slip) on the sharp interface.- AMReX Software Framework was used to develop the C++ code. For computation, the codes were parallelised using MPI.