The PSI-Center will refine present computational tools with sufficient physics, boundary conditions, and geometry to be calibrated with experiments to achieve predictive capabilities. Two 3D codes - NIMROD and MH4D - will be used.
NIMROD is a macroscopic simulation code having several of the critical features for modeling EC experiments. It has been used for numerical spheromak and RFP studies. NIMROD's algorithm solves compressible nonlinear magneto-fluid equations with electric-field terms selected to represent either the non-ideal single-fluid MHD model or two-fluid models of magnetized plasmas. Solution fields are marched from initial conditions with a semi-implicit algorithm for the MHD equations. The time centering of velocity is staggered from magnetic field, mass density, and temperature so that the integration of wave-like terms is symplectic. A semi-implicit operator is used to extend the range of numerical stability to arbitrarily large values of cΔt/h, where c is the magneto-acoustic wave speed, Δt is the time step, and h is the mesh spacing. Temporal truncation errors for wave propagation are then dispersive and not dissipative, which is important for simulating the nearly dissipation-free conditions encountered in astrophysical and laboratory plasmas. In addition, the MHD semi-implicit operator is based on the linear ideal-MHD energy integral, for accuracy at large Δt-values. Advection is treated with a predictor/corrector approach that is tailored for the semi-implicit algorithm.
NIMROD uses Lagrange-type finite elements to represent a non-periodic plane and truncated Fourier series for the periodic direction. The finite elements provide a flexible description of the poloidal plane, so NIMROD is suitable for a variety of laboratory configurations. However, spectral representation of the periodic direction limits it to configurations with a symmetric bounding wall. The code also has flexibility in the polynomial degree of the basis functions used for the finite elements, so that spatial convergence can be achieved through the most efficient combination of mesh resolution and basis function order. High-order basis functions have proven important for simulating the extremely anisotropic thermal transport associated with magnetized plasmas, particularly when the magnetic field is not aligned with the computational mesh as typically happens during relaxation calculations.
The complex multiply-connected 3D geometry of EC experiments like HIT-SI makes them very challenging to simulate with MHD codes. Most MHD codes currently available to the MFE research community are restricted to 2D boundaries or are written in toroidal coordinates and specialized to Tokamak-like geometries. An unstructured-mesh MHD code MH4D has been recently developed at SAIC with NASA funds. It was created for simulating astrophysical and space plasmas and includes only simple physics and boundary conditions. But it does have the right kind of mesh and data structure so it will be used as the starting point for our main simulation code. Boundary conditions will be modified to handle insulated flux conservers and the extra physics needed for EC experiments will be added. It will exactly conserve mass, momentum, energy and magnetic flux. It will be constructed to run efficiently in parallel on PC clusters and on NERSC computers. It will be made available, with documentation, to the entire fusion research community.