P. Colella

THE PLUTO CODE FOR ADAPTIVE MESH COMPUTATIONS IN ASTROPHYSICAL FLUID DYNAMICS

We present a description of the adaptive mesh refinement (AMR) implementation of the PLUTO code for solving the equations of classical and special relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids. We employ a conservative finite-volume approach where primary flow quantities are discretized at the cell-center in a dimensionally unsplit fashion using the Corner Transport Upwind (CTU) method. Time stepping relies on a characteristic tracing step where piecewise parabolic method (PPM), weighted essentially non-oscillatory (WENO) or slope-limited linear interpolation schemes can be handily adopted. A characteristic decomposition-free version of the scheme is also illustrated. The solenoidal condition of the magnetic field is enforced by augmenting the equations with a generalized Lagrange multiplier (GLM) providing propagation and damping of divergence errors through a mixed hyperbolic/parabolic explicit cleaning step. Among the novel features, we describe an extension of the scheme to include non-ideal dissipative processes such as viscosity, resistivity and anisotropic thermal conduction without operator splitting. Finally, we illustrate an efficient treatment of point-local, potentially stiff source terms over hierarchical nested grids by taking advantage of the adaptivity in time. Several multidimensional benchmarks and applications to problems of astrophysical relevance assess the potentiality of the AMR version of PLUTO in resolving flow features separated by large spatial and temporal disparities.

Mesh refinement for particle-in-cell plasma simulations: Applications to - and benefits for - heavy ion fusion

The numerical simulation of the driving beams in a heavy ion fusion power plant is a challenging task, and simulation of the power plant as a whole, or even of the driver, is not yet possible. Despite the rapid progress in computer power, past and anticipated, one must consider the use of the most advanced numerical techniques, if we are to reach our goal expeditiously. One of the difficulties of these simulations resides in the disparity of scales, in time and in space, which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g., fluid dynamics simulations) is the mesh refinement technique. They discuss the challenges posed by the implementation of this technique into plasma simulations (due to the presence of particles and electromagnetic waves). They will present the prospects for and projected benefits of its application to heavy ion fusion. In particular to the simulation of the ion source and the final beam propagation in the chamber. A collaboration project is under way at LBNL between the Applied Numerical Algorithms Group (ANAG) and the HIF group to couple the Adaptive Mesh Refinement (AMR) library (CHOMBO) developed by the ANAG group to the Particle-In-Cell accelerator code WARP developed by the HIF-VNL. They describe their progress and present their initial findings.

Performance of embedded boundary methods for CFD with complex geometry

In this paper, we discuss some of the issues in obtaining high performance for block-structured adaptive mesh refinement software for partial differential equations in complex geometry using embedded boundary/volume-of-fluid methods. We present the design of an adaptive embedded boundary multigrid algorithm for elliptic problems. We show examples in which this new elliptic solver scales to 1000 processors. We also apply this technology to more complex mathematical and physical algorithms for incompressible fluid dynamics and demonstrate similar scaling.

High-order finite-volume adaptive methods on locally rectangular grids

We are developing a new class of finite-volume methods on locally-refined and mapped grids, which are at least fourth-order accurate in regions where the solution is smooth. This paper discusses the implementation of such methods for time-dependent problems on both Cartesian and mapped grids with adaptive mesh refinement. We show 2D results with the Berger-Colella shock-ramp problem in Cartesian coordinates, and fourth-order accuracy of the solution of a Gaussian pulse problem in a polytropic gas in mapped coordinates.

Embedded boundary algorithms and software for partial differential equations

In this paper, we give an overview of a set of methods being developed for solving classical PDEs in irregular geometries, or in the presence of free boundaries. In this approach, the irregular geometry is represented on a rectangular grid by specifying the intersection of each grid cell with the region on one or the other side of the boundary. This leads to a natural conservative discretization of the solution to the PDE on either side of the boundary. Stable and robust hyperbolic and linear elliptic/parabolic solvers have been designed and implemented. Example applications of this approach are shown for compressible and incompressible gas dynamics problems in complex geometries, and for surface diffusion in a cell membrane.

Adaptive mesh simulations of multi-physics processes during pellet injection in tokamaks

We present the results of fully 3D adaptive mesh MHD simulations of fueling pellets injected into tokamaks. The Chombo framework for block structured local adaptive mesh refinement (AMR), extended to use the equilibrium magnetic coordinates, is employed to mitigate the problems due to the large range of spatial scales. Generalized upwinding techniques are employed to deal with sharp gradients. The modeling includes a semi-analytical kinetic treatment of the transport of electron energy flux which drives the ablation. We discuss the phenomenology of the mass redistribution processes involving the density equilibrating along field lines and transport across surfaces (in the large-major-radius direction).

A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov--Poisson Equation

Numerical solutions to the Vlasov--Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new particle-in-cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. H. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537]. It treats all of the stages of the standard PIC update---charge deposition, force interpolation, the field solve, and the particle push---with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. We demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2nd-order method. As expected, the 4th-order method can achieve accuracy comparable to that of the 2nd-order method and with considerably fewer resolution elements.

Modeling Coronal Mass Ejections with the Multi-Scale Fluid-Kinetic Simulation Suite

The solar eruptions and interacting solar wind streams are key drivers of geomagnetic storms and various related space weather disturbances that may have hazardous effects on the space-borne and ground-based technological systems as well as on human health. Coronal mass ejections (CMEs) and their interplanetary counterparts, interplanetary CMEs (ICMEs), belong to the strongest disturbances and therefore are of great importance for the space weather predictions. In this paper we show a few examples of how adaptive mesh refinement makes it possible to resolve the complex CME structure and its evolution in time while a CME propagates from the inner boundary to Earth. Simulations are performed with the Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS).