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Examples

HyperCloud ships with benchmark configurations covering the three built-in equations and both simulation pipelines.

Running an example

Pass the example function, uncalled, to a macro:

using HyperCloud
using PDEStudio
using GLMakie          # or WGLMakie for browser-based rendering

@plot euler_1d_sod     # run (or load from cache) and open the viewer

Without a viewer, for example on a cluster:

using HyperCloud

@sim euler_1d_sod

Available benchmarks

1D Sod shock tube (euler_1d_sod)

The classic Riemann problem for the Euler equations with $\gamma = 1.4$.

  • Data: $(\rho, u, p) = (1, 0, 1)$ for $x < 0$ and $(0.125, 0, 0.1)$ for $x > 0$, given to the IC as conservative states. SOD_LEFT and SOD_RIGHT hold them.
  • Grid: 330 jittered particles on $[-0.5, 0.5]$, fixed Dirichlet on the left and outflow on the right, tmax = 0.2.
  • Methods: the exact solution, first-order RK2Upwind1, RK2MUSCL2_VK (Venkatakrishnan limiter), and MUSCL with MOOD (RK2MUSCL2_U2_EPD1, RK4MUSCL4_U2_EPD1, plus the inactive RK2MUSCL2_U2_EPD2 and RK2MUSCL2_U1_EPD1).

1D kinetic Burgers (burgers_kinetic)

Compares a direct scheme with the kinetic relaxation formulation for Burgers' equation.

  • Data: a Gaussian pulse (a = 1, width = 1) on the periodic domain $[-5, 5]$ with 300 particles, up to tmax = 1.0. The pulse breaks at $t^* \approx 1.17$, so the run stays in the smooth regime where the exact solution is available.
  • Kinetic setup: speeds $\pm 2$ from generate_relax_params(2.0, 1, 1) and $\epsilon = 10^{-6}$.
  • Methods: RK2MUSCL2 (direct) and ARS222MUSCL2 (kinetic, IMEX).
  • Sweep: grid seeds 10, 100, 1000, 10000.

2D linear advection (advection_2d)

Transport of a Gaussian pulse along the diagonal.

  • Data: velocity $(1, 1)$ on the periodic square $[-5, 5]^2$ with $50 \times 50$ jittered particles, up to tmax = 10 (one full period in each direction).
  • Methods: RK2MUSCL2 against the exact solution from characteristic tracing.
  • Sweep: grid seeds 10, 100, 1000, 10000.

Writing your own

Copy one of the example functions, change the parameters, and run it with @sim or @plot. The Configuration Reference lists every key. Saving the function as my_case.jl in a folder listed in CONFIG_SEARCH_PATHS lets you call @sim my_case from any session without including the file first.