Slope Limiters for High Order Finite Volume Schemes

Graduate Student Seminars
Feb 6, 2024
12:30 - 1:30 pm
Fine Hall 214

In this talk I will discuss the finite volume method and its application to initial value problems of hyperbolic PDE. Because of Runge's phenomenon, a high order finite volume scheme will produce unphysical oscillations in the presence of shocks. Furthermore, we request that our numerical solution respects the maximum principle of the initial condition. That is, our numerical solution should be bounded at each step by the minimum and maximum of the initial condition. Slope limiters are used to circumvent this issue. We will discuss two slope limiting paradigms, the importance of quadrature rules, and many other parameters which affect the solution quality.