COSAM » Events » 2015 » January » Colloquium: Dr. David Seal, Department of Mathematics, Michigan State University

Colloquium: Dr. David Seal, Department of Mathematics, Michigan State University
Time: Jan 28, 2015 (04:00 PM)
Location: Parker Hall 249

Details:

Dr. David Seal, Department of Mathematics, Michigan State University

Abstract: Hyperbolic conservation laws describe a large class of problems including applications in astrophysics, aerospace engineering, storm surge modeling and electromagnetics. Difficulties in developing numerical methods for these problems include the ability of the scheme to capture shocks, the necessity to satisfy a discrete conservation of physical quantities such as mass, momentum and energy, and for plasmas, the ability to retain divergent free magnetic fields. High-order methods for hyperbolic conservation laws have seen an increasing amount of attention for over the past several decades given their ability to obtain high-order accuracy with far fewer unknowns. 

High-order methods require high-order time stepping that have traditionally been classified into two disparate categories: i) the method of lines formulation which starts by discretizing the spatial variables, and then evolves a system of ODEs with an appropriate time-integrator, or ii) Lax-Wendroff discretizations that immediately convert temporal Taylor series into discrete spatial derivatives. In this talk, we resolve this false dichotomy by introducing multiderivative methods as a unifying class. Our methods are constructed through a flux modification, and therefore are automatically mass conservative and have the capacity to reduce computational complexity, including i) a reduction in the number of characteristic variable projections, ii) the number of applications of expensive limiters, and iii) a reduction in the effective stencil size. We present multidimensional results that include positivity preservation for Euler and MHD equations, as well as highlight our flux modifications by demonstrating a new limiter.


 
Faculty host: Yanzhao Cao





Last updated: 09/11/2015