JURHIATA

A finite-volume moving-mesh code for compressible hydrodynamics (HD).

Code Summary

JURHIATA is a moving-mesh astrophysical code developed in C++ for high-fidelity HD simulations on Voronoi meshes. The current production baseline is HD with MUSCL-Hancock reconstruction and HLLC fluxes, validated through Sod and Sedov benchmark tests.

Numerics

Finite-volume Godunov method on 3D Voronoi cells.

Accuracy

Second-order in space and time through MUSCL-Hancock.

Parallel Baseline

Hybrid OpenMP + MPI implementation completed on CPU.

Roadmap

Stage-1 GPU acceleration and Stage-2 multi-physics modules.

Hydrodynamics Equations (Euler System)

JURHIATA currently solves the compressible Euler equations in conservative form:

∂ρ/∂t + ∇·(ρv) = 0
∂(ρv)/∂t + ∇·(ρv⊗v + pI) = 0
∂E/∂t + ∇·[(E + p)v] = 0
E = p/(γ - 1) + 0.5 ρ |v|2

MUSCL-Hancock Workflow

  1. Build Voronoi geometry (volumes, areas, normals, centroids).
  2. Compute gradients and apply slope limiting for monotonicity.
  3. Reconstruct left/right interface states and predict half-step values.
  4. Solve Riemann problems at moving faces and compute fluxes.
  5. Update conserved variables and enforce positivity floors.
  6. Move mesh generators and rebuild tessellation for the next timestep.

Hydrodynamic Riemann Solvers

Solver Primary Use Wave Model Notes
Exact (Euler) Reference and validation runs Iterative exact 1D Riemann solution Used for hydro flux verification and regression checks.
HLLC Default hydrodynamic production solver Three-wave model (SL, S*, SR) Good balance of robustness and accuracy for strong shocks.

Moving Mesh with Voro++

JURHIATA computes Voronoi geometry (cell volumes, face areas, normals, centroids) with Voro++. Mesh generators move with the local flow in an ALE-style formulation to reduce advection error while preserving a conservative finite-volume update.

Δti = CFL hi / ( |v - vface| + cs )

Validation: Sod and Sedov

JURHIATA Sod validation panel
Sod Shock Tube: density, velocity, and pressure profiles plus density slice from the proposal-quality panel.
JURHIATA Sedov validation panel
Sedov-Taylor Blast: radial profile and density slice panel used for proposal validation evidence.

Current Status

  • HD baseline validated with Sod and Sedov tests.
  • Hybrid parallelization OpenMP + MPI completed on CPU.
  • GPU acceleration is the next implementation stage.
  • MHD and additional physics modules are planned for later stages.

Selected References

  1. Springel, V. (2010), E pur si muove: moving-mesh hydrodynamics with AREPO, MNRAS 401, 791.
  2. Toro, E. F. (2009), Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer.
  3. Chang, P., Wadsley, J., Quinn, T. (2017), MANGA: a moving-mesh hydrodynamic solver for ChaNGa, MNRAS 471, 3577.
  4. Rycroft, C. H. (2009), Voro++: A three-dimensional Voronoi cell library in C++, Chaos 19, 041111.