added gresho vortex

Author: pmocz

examples/README.md

@@ -1,3 +1,3 @@
 # Adirondax Examples
 
-Simple examples to demonstrate adirondax' capabilities and help you get started with your own simulations
+Simple examples to demonstrate the capabilities of adirondax and help you get started with your own simulations

examples/gresho/README.md

@@ -0,0 +1,27 @@
+# Gresho
+
+Simulate the Gresho Vortex
+
+Philip Mocz (2025)
+
+Usage:
+
+```console
+python gresho.py
+```
+
+Takes around 10 seconds to run on my macbook (cpu).
+
+
+## Simulation snapshots
+
+<div style="display:flex;flex-wrap:wrap;gap:8px">
+  <img src="output.png" alt="output" width="45%"/>
+</div>
+
+
+## References
+
+[Gresho, P.M.; Chen, S.T.; On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. II - Implementation. International Journal for Numerical Methods in Fluids (1990)](https://ui.adsabs.harvard.edu/abs/1990IJNMF..11..621G)
+
+[Liska, R. ; Wendroff, B.; Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations. SIAM Journal on Scientific Computing (2003)](https://ui.adsabs.harvard.edu/abs/2003SJSC...25..995L)

examples/gresho/gresho.py

@@ -0,0 +1,103 @@
+import jax.numpy as jnp
+
+# TODO: REMOVE THE FOLLOWING LINES
+import sys
+
+sys.path.append("../../")
+
+import adirondax as adx
+import time
+import matplotlib.pyplot as plt
+
+"""
+Simulate the Gresho Vortex
+
+Philip Mocz (2025)
+"""
+
+
+def set_up_simulation():
+    # Define the parameters for the simulation
+    nx = 128
+    nt = -1
+    t_stop = 3.0
+
+    params = {
+        "physics": {
+            "hydro": True,
+        },
+        "mesh": {
+            "type": "cartesian",
+            "resolution": [nx, nx],
+            "box_size": [1.0, 1.0],
+        },
+        "time": {
+            "span": t_stop,
+            "num_timesteps": nt,
+        },
+        "output": {
+            "num_checkpoints": 100,
+            "save": False,
+            "plot_dynamic_range": 2.0,
+        },
+        "hydro": {
+            "eos": {"type": "ideal", "gamma": 5.0 / 3.0},
+            "slope_limiting": True,
+        },
+    }
+
+    # Initialize the simulation
+    sim = adx.Simulation(params)
+
+    # Set initial conditions
+    sim.state["t"] = 0.0
+    X, Y = sim.mesh
+    R = jnp.sqrt((X - 0.5) ** 2 + (Y - 0.5) ** 2)
+    def v_phi(r):
+        return jnp.where(
+            r < 0.2,
+            5.0 * r,
+            jnp.where(r < 0.4, 2.0 - 5.0 * r, 0.0),
+        )
+    def P0(r):
+        return jnp.where(
+            r < 0.2,
+            5.0 + 12.5 * r**2,
+            jnp.where(r < 0.4, 9.0 + 12.5 * r**2 - 20.0 * r + 4.0 * jnp.log(r / 0.2), 3.0 + 4.0 * jnp.log(2.0)),
+        )
+    vx = -v_phi(R) * (Y - 0.5) / (R + (R==0))
+    vy = v_phi(R) * (X - 0.5) / (R + (R==0))
+    sim.state["rho"] = jnp.ones(X.shape)
+    sim.state["vx"] = vx
+    sim.state["vy"] = vy
+    sim.state["P"] = P0(R)
+
+    return sim
+
+
+def make_plot(sim):
+    # Plot the solution
+    plt.figure(figsize=(6, 4), dpi=80)
+    v_phi = jnp.sqrt(sim.state["vx"]**2 + sim.state["vy"]**2)
+    plt.imshow(v_phi.T, cmap="jet", vmin=0.0, vmax=1.0)
+    plt.gca().invert_yaxis()
+    plt.colorbar(label="v_phi")
+    plt.tight_layout()
+    plt.savefig("output.png", dpi=240)
+    plt.show()
+
+
+def main():
+    sim = set_up_simulation()
+
+    # Evolve the system
+    t0 = time.time()
+    sim.run()
+    print("Run time (s): ", time.time() - t0)
+    print("Steps taken:", sim.steps_taken)
+
+    make_plot(sim)
+
+
+if __name__ == "__main__":
+    main()

examples/gresho/output.png

@@ -18,3 +18,8 @@ Takes around 6 seconds to run on my macbook (cpu).
 <div style="display:flex;flex-wrap:wrap;gap:8px">
   <img src="output.png" alt="output" width="45%"/>
 </div>
+
+
+## References
+
+[Springel, V.; E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh. Monthly Notices of the Royal Astronomical Society (2020)](https://ui.adsabs.harvard.edu/abs/2010MNRAS.401..791S)

examples/kelvin_helmholtz/README.md

@@ -18,3 +18,8 @@ Takes around 55 seconds ('llf') / 105 seconds ('hlld') to run on my macbook (cpu
 <div style="display:flex;flex-wrap:wrap;gap:8px">
   <img src="output.png" alt="output" width="45%"/>
 </div>
+
+
+## References
+
+[Orszag, S.A.; Tang, C.M.; Small-scale structure of two-dimensional magnetohydrodynamic turbulence. Journal of Fluid Mechanics (1979)](https://ui.adsabs.harvard.edu/abs/1979JFM....90..129O)

examples/orszag_tang/README.md

@@ -18,3 +18,8 @@ Takes around 9 seconds to run on my macbook (cpu).
 <div style="display:flex;flex-wrap:wrap;gap:8px">
   <img src="output.png" alt="output" width="45%"/>
 </div>
+
+
+## References
+
+[Springel, V.; E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh. Monthly Notices of the Royal Astronomical Society (2020)](https://ui.adsabs.harvard.edu/abs/2010MNRAS.401..791S)