(Dust) Particles in Athena++ Chao-Chin Yang Zhaohuan Zhu University - - PowerPoint PPT Presentation

(Dust) Particles in Athena++

Chao-Chin Yang Zhaohuan Zhu

University of Nevada, Las Vegas

James Stone

Princeton University

Dust-Gas Dynamics

• Lagrangian formulation
• Lagrangian vs. two fluids
• Particle-Mesh method
• Gas properties on each particle
• Averaged particle properties in each gas

cell

• Triangle-Shaped Cloud (TSC)
• Stopping time ts = 0: tracer particles

d ⃗ v p dt = ⃗ u g − ⃗ v p ts d ⃗ u g dt = ( ρp ρg ) ⃗ v p − ⃗ u g ts

Nonlinear Streaming Instability

Global Spherical-polar Disk

Current Status

• Van Leer integrator with any reconstruction
• Particle-Mesh: both ways
• Static mesh refinement
• Message Passing Interface (MPI)
• Coordinates: Cartesian ready; spherical-polar under testing
• Useful: OpenMP threads block by block, and hence particles inside

Hierarchical Design

• Class Particles
• Abstract base class
• Data structure & maintenance
• Integration with task list
• Communication
• Send/receive particles
• Send/receive particle-mesh
• I/O
• Class DustParticles
• Derived application class
• New specific properties
• Source terms
• Class ParticleMesh
• Utility class
• Interpolation and assignment
• Communication
• Deposit onto MeshBlock

Data Structure

• Number of properties requested before MeshBlock construction
• Integer properties: Particle ID, …
• Real properties
• Dynamical variables: Position (xp, yp, zp), Velocity (vpx, vpy, vpz), etc.
• Auxiliary variables: always existent and follows each particle
• Working arrays: garbage after each stage
• Shorthands (shallow copies)
• Number of particles in each MeshBlock dynamically maintained
• npar: current number of particles
• nparmax: capacity of the particle arrays

AthenaArray<> prop(nvar, nparmax); Void Particles::UpdateCapacity(int new_nparmax);

Outputs

• Particle properties on mesh
• Can be output in any format

available to MeshBlock

• Number density “np”
• Velocity “vp” with respect to

Coordinates.

• Mass density “rhop”
• “prim” = (“rhop”,

“vp1”, “vp2”, “vp3”)

• Data of individual particles
• Only formatted table
• Restart files
• Not ready
• Inhomogeneous data size

between MeshBlocks

Uniform (Oblique) Streaming

Linear Mode of the Streaming Instability

10−14 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 Error ux L∞ ≈ 1.1 × 10−6(∆/λ)1.91 L2 ≈ 6.0 × 10−7(∆/λ)1.93 uy L∞ ≈ 1.3 × 10−6(∆/λ)1.91 L2 ≈ 6.5 × 10−7(∆/λ)1.91 uz L∞ ≈ 1.2 × 10−6(∆/λ)1.92 L2 ≈ 6.0 × 10−7(∆/λ)1.93 ρg L∞ ≈ 5.9 × 10−9(∆/λ)1.82 L2 ≈ 3.4 × 10−9(∆/λ)1.86 10−3 10−2 10−1 ∆/λ 10−14 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 Error vp,x L∞ ≈ 1.1 × 10−6(∆/λ)1.91 L2 ≈ 5.7 × 10−7(∆/λ)1.92 10−3 10−2 10−1 ∆/λ vp,y L∞ ≈ 1.3 × 10−6(∆/λ)1.90 L2 ≈ 6.8 × 10−7(∆/λ)1.91 10−3 10−2 10−1 ∆/λ vp,z L∞ ≈ 1.2 × 10−6(∆/λ)1.92 L2 ≈ 6.4 × 10−7(∆/λ)1.92 10−3 10−2 10−1 ∆/λ ρp L∞ ≈ 7.4 × 10−5(∆/λ)1.87 L2 ≈ 4.7 × 10−5(∆/λ)1.94

Streaming instability — LinA mode — integrator = vl2 — xorder = 3 — 4 particles/cell

TODOs

• Spherical-polar and cylindrical coordinates
• Particle integrator in sync with any time integrator
• Non-uniform grid
• Restart files
• Boundary conditions for particles
• Currently, only periodic or removed
• Adaptive mesh refinement
• More Particles outputs
• Optimization and documentation