Thirty years at LANL – A Case Study

Abstract: This talk has two parts.  In the first, part I will give an overview of my 30 years career at the Los Alamos National Laboratory (LANL).  It will include a timeline and overview of my main scientific achievements: developing mimetic finite difference methods, development of different aspects of multimaterial arbitrary Lagrangian-Eulerian methods (ALE), reconnection-based ALE, and so on.

In second part, I will describe recent research related to moments-based interface reconstruction.We present a new moment-of-fluid (MOF2) interface reconstruction method.  It uses the zeroth, first, and second moments of the fragment of material inside a cell of the mesh to reconstruct a convex material polygon, or a union of convex polygons, that approximate the respective material fragment.  The new method requires information about the material moments only for the cell under consideration.  The MOF2 method allows to exactly reproduce several convex shapes: corners, filaments, and some concave shapes: cell complements to corners and filaments.

Interface reconstruction is formulated as a local (for each cell), non-linear, and equality constrained optimization problem, which does not require additional communication and allows for an efficient parallel implementation.  We present an extensive set of test problems, both for interface reconstruction on a single cell, and for reconstruction of a variety of shapes on a variety of meshes.  We describe how to perform two-material advection using the MOF2 method and present the results for the classical advection tests.  We also show the examples of material interface remapping needed in the framework of multi-material arbitrary Lagrangian-Eulerian methods and give a brief description of a procedure that can be used to update the material moments on the Lagrangian stage of those methods.

Speaker’s Bio:  Mikhail Shashkov is currently Scientist 6 at Continuum Models and Numerical Methods Group at X-Computational Physics Division at LANL.  His research interests include developing mimetic finite difference methods and development of different aspects of multi-material arbitrary Lagrangian-Eulerian methods.  He received his Ph.D. in Applied Mathematics from the Keldysh Institute of Applied Mathematics in Moscow, Russia in 1979 and Habilitation from Moscow State University in 1990.  He is LANL and Society for Industrial and Applied Mathematics Fellow.  His Google Scholar - h-index:59, with 12783 citations.  According to Research.com he ranked in Mathematics: US-301, World-581, D-Index-55.