Applications Development Plan

Introduction

Initial Applications Projects

• An adaptive mesh refinement MHD code for tokamak simulation. The motivating physics example is the simulation of the internal kink mode in a tokomak with arbitrary aspect ratio. In this problem, temperature variations in the plasma lead to small-scale regions with intensified currents, which lead to nonlinear instabilities that may either disrupt the plasma, or saturate to produce macroscopically stable periodic behavior. We will develop an adaptive mesh capability capable of resolving the multiple scales generated by the intensified currents, and the highly localized non-ideal physics of magnetic reconnection that drive the nonlinear phase of the instability.
• An electrostatic AMR-PIC code for accelerator modeling. We will replace the uniform-grid finite difference calculation traditionally used with an adaptive mesh refinement finite-difference Poisson solver. We will also couple this to a Shortly-Weller Cartesian grid treatment of irregular Dirichlet boundaries. The use of adaptive grids for PIC calculations is a natural extension, since grid resolution requirements typically are greatest in the neighborhood of large particle densities, particularly when particles are near irregular boundaries. We will integrate this package into existing simulation codes for accelerator design as it arises in RF accelerators and in heavy-ion fusion.
• Direct Numerical Simulation of Combustion We will develop a releaseable package of our 2D and 3D parallel AMR code for unsteady laminar combustion with detailed chemistry, suitable for use by researchers in the combustion community that are not necessarily experts in computational fluid dynamics. This will require us to address three issues. First, we will need to make improvements to the robustness of some of the numerical algorithms, particularly in the area of linear systems solvers for the elliptic and parabolic problems. We will develop some user interface tools, including problem definition, error control specification, as well as providing access to the visualization and analysis tools we have developed. Finally, we will write user documentation for the package.

Follow-on Applications Projects

• Electrostatic and Electromagnetic Particle Codes. This would be a flexible suite of codes to simulate Vlasov-Poisson and Vlasov-Maxwell problems, based on adaptive mesh refinement for the field solver. Options would include choice of representation (e.g. electrostatic potential, electric field); choice of interpolation methods for transferring information between the particles and the grid (e.g. area-weighting, MLC); choice of field discretization (e.g. second-order, fourth-order Mehrstellen), as well as an option for representing the effects of irregular geometry using embedded boundaries.
• Hybrid fluid / kinetics solvers for time-dependent problems in MHD. This would extend the AMR MHD fluids code to the case of hybrid fluid-particle models. For example, energetic ion species produced by fusion reactions in the plasma are represented using a gyrokinetic model, with the electrons and bulk ions represented by a fluid. This is the first of a hierarchy of such models, that range up to using a phase-space description of all of the ions, with the fluid representation used only for the electrons.
• Compressible jets for laser-plasma accelerators. We would develop a capability for simulating the time-dependent fluid dynamics of gas jets and plasma formation as arises in the design of laser-plasma accelerators. Laser ionization of the gas plume serves as the plasma source in these accelerators, and optimal tailoring of the plasma density through judicious jet design and these use of channel-forming lasers is necessary to enhance accelerator performance . In this problem, it is necessary to compute the fully compressible viscous flow in the injector, as well as the free-boundary flow of the jet as it moves into a near-vacuum ambient. It is also necessary to model the expansion of a hot plasma core into a surrounding neutral gas, including the formation of shocks near the gas-plasma interface. The code would use an embedded boundary method for the compressible Navier-Stokes equations to represent the flow in the injector; a volume-of-fluid representation of the free boundary between the jet and the vacuum; and adaptive mesh refinement. The results of these simulations will be benchmarked against experiments carried out at LBNL.
• Multiphase Combustion. We will extend the 3D DNS combustion capability to the case of spray combustion. This DNS capability will focus on dilute fuel sprays with relatively low velocities that are meant to represent the later stages of a direct injection spray. In keeping with the DNS approach, many of the modeling assumptions will be removed from the spray routines including the parcel assumption. Individual spray drops will be simulated in a representative region of a spray being injected into a turbulent environment. The fuel drops will be somewhat simplified (e.g. single component and simple distortion models) but they will be sufficient to address fundamental spray mixing problems.
• Combustion in Irregular Geometries. Many fundamental combustion experiments are performed in modestly irregular, but still irregular geometries, e.g. flame holders, bomb combustors, and bluff-body flames. We would develop a three-dimensional direct numerical simulation capability for such geometries. It would be a generalization of the AMR combustion capability developed, using the embedded boundary approach to represent the geometry.