FLUME

FLUME (Fluid Laboratory for Unsteady Multiphysics at Exascale) is the compressible-flow application of ADAM: compressible Euler, Navier–Stokes and ideal MHD with external gravity, self-gravity and sink particles, ideal, isothermal and barotropic gases, radiative cooling, passive scalars and immersed boundaries, solved with high-order WENO finite differences on block-structured adaptive grids (static and runtime AMR, multi-realm forests), on CPUs (MPI + OpenMP) and on GPUs (MPI + OpenACC, or OpenMP offload). It supersedes the deprecated CHASE.

What is implemented

Area	Capabilities	Details
Physics	Compressible Euler (optionally with dual energy and up to 4 passive scalars); ideal MHD with mixed GLM or EGLM divergence cleaning (or without control, for diagnostics); ideal, isothermal or barotropic gas; viscosity, heat conduction and Ohmic resistivity; external gravity and self-gravity; optically thin radiative cooling; sink particles	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, LLF/HLL/HLLD for MHD); cell-based positivity limiter	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, AMR at initialisation and during the run (box, gradient, Löhner 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	25 initial conditions (Riemann problems, vortices, Shu–Osher, Orszag–Tang, rotor, field loop, linear waves, exact viscous states, atmospheres, self-gravitating spheres and clouds, ...), 7 boundary conditions (no-slip and isothermal walls, hydrostatic faces under gravity 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 M13 are complete:

Milestone	Content
M1 #35	compressible Euler
M2 #41	ideal MHD with GLM
M3 #47	the Riemann-solver scheme (weno-riemann, Euler and MHD), EGLM cleaning, the positivity-preserving limiter
M4 #65	viscosity, heat conduction (no-slip walls) and Ohmic resistivity, conservative across AMR seams and realms
M5 #74	runtime AMR ([amr] frequency, setting it up), restarts across regrids
M6 #68	seam accuracy and divergence at 2:1 faces
M7 #73	external gravity
M8 #81	self-gravity, periodic and isolated, uniform and AMR (#87)
M9 #91	dual energy (euler-de) and the Jeans refinement marker
M10 #92	passive scalars
M11 #93	optically thin radiative cooling
M12 #94	sink particles
M13 #100	isothermal and barotropic equations of state, Euler and MHD

Every milestone runs on both backends.

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, quadtrees and binary trees, the seam normal to a refined axis, #71); all realms advance with one time step (no subcycling).