|Date: Friday, February 09, 2018
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: A new approach to numerical conservation laws
Abstract: The numerical solution of hyperbolic conservation laws, either by Finite Volume or Finite Element methods, rests largely on representing the solution by smooth basis functions within each element, leaving discontinuities at the boundaries. The discontinuities are resolved by solving one-dimensional Riemann problems. The basic idea was introduced by Godunov in 1959, and since then has been accepted as a natural, almost inevitable, approach. In this talk, the representations will be continuous and no Riemann problems will be solved. The emphasis will be on distinctive handling of the advective and non-advective disturbances, with initial reference to the advective-acoustic structure of the Euler equations. In the usual approach, this distinction is not given prominence, because in one dimension the advective and acoustic modes behave very similarly. Here, we recognize the considerable differences found in higher dimensions. Advection is dealt with by semi-Lagrangian Streamline tracing, and acoustics by adapting Poisson's solution to the Initial-Value Problem for the scalar wave equation. These elements are combined to give a third-order accurate, fully explicit, maximally stable and conservative method. Initial experiments suggest that it provides accuracy comparable to other high-order methods at substantially reduced cost.
Speaker: Phil Roe
Institution: University of Michigan, Aerospace Engineering
Event Organizer: AIM Seminar Organizers firstname.lastname@example.org