Main Research Teaching

Research Activities

The main thrust of my research is the development of Asymptotic Preserving (AP) schemes for physical models. An AP scheme (a term first coined by Shi Jin) is a scheme that captures, at the discrete level, the asymptotic passage from one model to another. These schemes allow (stable) under-resolution of features that are not important in asymptotic regimes, and can be used in a wide range of regimes without any arbitrary cutoffs or domain decomposition. The concept can be applied to a wide range of applications with multiscale character - for example, underwater explosions (gas-water mixtures), aerodynamics, and particle transport and heat transfer in problems with multiple materials, such as radiation dosing in cancer therapy.

Projects

• I am currently working with my advisor, Shi Jin, and Jian-Guo Liu (Duke) on Mach number uniform asymptotic preserving schemes for compressible flows.
  
  
• I am working with Cory Hauck (Oak Ridge National Laboratory) on asympotic preserving schemes for moment methods in neutron transport and radiative transfer. We are especially interested in the asymptotic properties of schemes in regimes with spatially varying and discontinuous material properties.
  
  
• I am also working with Cory Hauck (Oak Ridge) and Rob Lowrie (Los Alamos National Laboratory) on the asymptotic properties of Discontinuous Galerkin (DG) schemes in the low Mach number limit of compressible flow.
  
  
• Notes on Integrating Factor Methods for nonlinear wave equations (Spring 2007)

Publications

• J. Haack, S. Jin, and J.-G. Liu, An all-speed asymptotic preserving scheme for compressible flow, in preparation.
• J. Haack, C. Hauck., Oscillatory Behavior of Asymptotic-Preserving Splitting Methods for a Linear Model of Diffusive Relaxation, Los Alamos Report LA-UR-08-0571, Kinetic and Related Models, 1, 573--590, 2008.

Research Interests

• Scientific Computing
• Multiscale Methods
• Kinetic Equations
• Fluid Dynamics

Talks, Presentations

• Organizer (2008 - ), multiple talks given, UW Madison Applied Math Graduate Participation Seminar
• Natural Frequencies of a Fluid Carrying Plate PIMS Graduate Industrial Mathematics Modelling Camp, 2007
• Mathematical Techniques for Preconceptual Design, IMA Mathematical Modeling in Industry XI, 2007
• All Speed Asymptotic Preserving Schemes for Compressible Flows. CNLS summer student seminar, Los Alamos National Laboratory, July 8, 2008
• Parity-based Splitting Schemes for the Time-dependent $P_N$ Equations Center For Nonlinear Studies, Los Alamos National Laboratory, August 14, 2008
• A Mach-number uniform asymptotic-preserving scheme for the isentropic Euler equations - Mathematics and Its Applications Seminar, University of Illinois-Chicago, April 22, 2009
• A Mach-number uniform asymptotic-preserving scheme for the isentropic Euler equations - 2009 SIAM Annual Meeting, Denver, July 7, 2009
• Discontinuous Galerkin methods for compressible gas dynamics in the incompressible limit, CNLS summer student seminar, Los Alamos National Laboratory, August 12, 2009.

Links

UW Applied Math
Applied GPS