High resolution numerical approximations of hyperbolic conservation laws and Hamilton-Jacobi equations
Abstract:
High order accurate shock capturing schemes are designed to resolve complex shock dynamics with high accuracy in space and time avoiding spurious oscillations near discontinuities. We analyze the use of hyperbolas and parabolas as basic functions for the design of piecewise smooth reconstruction procedures and discuss the advantage of applying slope limiters to control the total variation growth. We propose the use of 'power' limiters to improve the behavior of the piecewise hyperbolic method and the weighted essentially non-oscillatory (WENO) parabolic method. We present a set of numerical experiments showing the different approaches for Euler equations of gas dynamics. We extend the discussion to the approximation of the viscosity solution of Hamilton-Jacobi equations with applications to the level set reinitialization.
Applied Mathematics Seminar