FLUME

FLUME (Fluid Lorentz-coupled Unsteady Magnetohydrodynamic Equations) is the compressible-flow and magnetohydrodynamics application of ADAM. It solves the compressible Euler equations and the ideal MHD equations with high-order WENO finite differences on block-structured adaptive grids, on CPUs (MPI + OpenMP) and on GPUs (MPI + OpenACC), and it supersedes the deprecated CHASE.

What is implemented

Area	Capabilities	Details
Physics	Compressible Euler; ideal MHD with mixed GLM divergence cleaning (or without control, for diagnostics); ideal gas	Physical models
Space	WENO flux splitting (weno, orders 3–9, characteristic or conservative); WENO interpolation + Riemann flux + high-order correction (weno-riemann, LLF/HLL/HLLC for Euler)	Numerical methods
Time	SSP and low-storage Runge–Kutta, CFL time step (with the GLM cleaning speed)	Numerical methods
Grid	Octree/quadtree of Cartesian blocks, initialisation-time AMR (box, gradient and solid markers), 2:1 coarse–fine faces with conservative reflux	Numerical methods
Geometry	Immersed boundary for static solids (Euler)	Numerical methods
Coupling	Multi-realm runs glued by a forest manifest	Numerical methods
Setup	17 initial conditions (Riemann problems, vortices, Shu–Osher, Orszag–Tang, rotor, field loop, linear waves, exact viscous states, ...), 6 boundary conditions (no-slip walls included)	Initial conditions, Boundary conditions
Input	One INI file per realm, every value checked	Input reference
Output	XDMF + HDF5 checkpoints (ParaView), restart, slices, residual, conservation and div(B) histories	Input reference
Verification	Exact solutions, convergence orders, symmetry and conservation oracles on both backends	Verification gallery

Status. Milestones M1 to M5 are complete: M1 Euler (#35), M2 ideal MHD with GLM (#41), M3 (#47) the Riemann-solver scheme (weno-riemann, Euler and MHD), the energy-consistent EGLM cleaning and a positivity-preserving limiter, and M4 (#65) the dissipative terms: compressible Navier–Stokes (viscosity and heat conduction, 4th-order conservative fluxes, no-slip walls) for every model and Ohmic resistivity for MHD, on both backends, conservative across AMR seams and realms (second order at a 2:1 seam, as the inviscid fluxes). M5 (#74) runtime AMR: both backends regrid during the run ([amr] frequency), with a conservative limited prolongation, combined markers (gradient, Löhner, box, solid) and restarts across regrids (setting it up).

Quick start

Build (FoBiS, from the repository root):

fobis build --mode flume-cpu-gnu                         # CPU backend
fobis build --mode flume-fnl-nvf --varset local_nvf      # GPU backend (OpenACC, NVIDIA HPC SDK)

Run the Sod shock tube of the verification suite:

cd src/tests/flume/verification/sod
mpirun -np 2 ../../../../../exe/adam_flume_cpu sod-x.ini

The run writes sod-x-<iteration>.xdmf (open it with ParaView) and the residual and conservation histories. The input reference explains every key of sod-x.ini. To run the same problem with the Riemann-solver scheme, change its [numerics] section to

[numerics]
scheme_space             = weno-riemann
reconstruction_variables = characteristic
riemann_solver           = hllc
flux_correction          = 6th
flux_correction_sensor   = weno
reflux                   = .true.

./check.sh in the same directory runs the three directions and compares them with the exact solution.

Pages

• Physical models: equations, thermodynamics, eigensystems, GLM cleaning, time-step bound.
• Numerical methods: finite differences, WENO, flux splitting, Riemann solvers and correction, time integration, AMR and reflux, immersed boundary, multi-realm.
• Initial conditions and boundary conditions: formulas, keys, examples.
• Input reference: every section and key, with two complete inputs.
• Verification gallery: the test cases with figures and measured results.
• Source layout: common, CPU backend, FNL backend.

Known limitations

• Seam div(B). A cell-centred $\mathbf{B}$ cannot be kept divergence-free across a 2:1 coarse–fine face (Tóth & Roe 2002): the seams inject a truncation-level $\mathrm{\nabla }\cdot \mathbf{B}$, which GLM keeps bounded; seam_max_divb in the div(B) history monitors it.
• Positivity at very low plasma β. The floors alone do not hold it: without the positivity limiter the flux-splitting scheme stops on the Balsara–Spicer blast ($\beta =2.5\cdot {10}^{-4}$) at step 3 and on the Wu–Shu blast ($\beta =2.51\cdot {10}^{-6}$) at step 1. With [numerics] positivity_limiter = cell (M3, #47) both schemes run both to the end (positivity limiter). On the flux-splitting path at $\beta \lesssim {10}^{-3}$ the point symmetry and the CPU–FNL agreement then hold only to a grid-scale instability (#77, MHD blast symmetry); where they matter, use scheme_space = weno-riemann with riemann_solver = hlld.
• GLM damping and reflux. With damping, $\int \psi$ is not conserved across 2:1 faces; the 8 physical integrals are.
• The GPU backend copies the coarse–fine seam faces to the host at every stage (the flux register is host-side), in one transfer for all the faces of a rank since #90.
• Inter-realm seams join cells of the same size (mirror) or across a 2:1 jump (refined, #52; octrees only, quadtrees are refused, #71); all realms advance with one time step (no subcycling).