Title: A comprehensive spatio-temporal numerical scheme for fully implicit 3D extended MHD

Speaker: Luis Chacon (Speaker) and Dana Knoll, Los Alamos National Laboratory

Date/Time: Monday, January 31, 2005, 1:00-2:00 pm

Location: Building 980, Room 95 (Sandia NM)

Brief Abstract: An accurate and efficient numerical solution of the magnetohydrodynamics (MHD) in general geometries is of the essence for the adequate simulation and proper design of the next generation MFE fusion reactors. Temporally, a fully implicit treatment is desirable (vs. an explicit or semi-implicit treatment) to effectively deal with the numerical stiffness of MHD fast waves without compromising accuracy. Spatially, the desired scheme should be conservative, solenoidal in the magnetic field to machine precision, stable in the absence of numerical and physical dissipation, and suitable for mesh adaptivity in curvilinear geometries. In this talk we will discuss the details of both the spatial and temporal aspects of a comprehensive numerical scheme that satisfies the requirements outlined above. In particular, we will provide details of a novel cell-centered finite-volume 3D MHD spatial scheme that is solenoidal, conservative, non-dissipative, stable, and second-order accurate even in curvilinear grids. We will also discuss the current status in the development of a fully implicit Newton-Krylov algorithm for the compressible 3D extended MHD model, focusing on the details of the physics-based preconditioning concept. We will present results that demonstrate optimal solver scalability under grid refinement and time step size for the resistive MHD system.