This project is to numerically solve fractional Laplace equations and related equations. The major numerical methods we use are Jacobi-spectral methods. Our ultimate goal is to numerically solve a turbulence testbed problem. To achieve our goal, we first establish fractional Laplacian of Jacobi polynomials and choose proper test functions for our spectral methods. We start from linear steady and unsteady equations and then solve nonlinear unsteady equations. For unsteady equations, we have to take a different test function than that for steady equations to avoid singularity of the resulting linear systems.
Worcester Polytechnic Institute
Major Qualifying Project
All authors have granted to WPI a nonexclusive royalty-free license to distribute copies of the work, subject to other agreements. Copyright is held by the author or authors, with all rights reserved, unless otherwise noted.