[example] Request to add my code into examples (#6185)

I added my code for ti.example. You can see details of my example here
https://forum.taichi.graphics/t/topic/2924

This is a 1D simulation of "two-stream instability" in Plasma Physicis.

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

python/taichi/examples/simulation/two_stream_instability.py

@@ -0,0 +1,93 @@
+# Authored by Luhuai Jiao
+# This is a 1D simulation of "two-stream instability" in Plasma Physicis.
+# Some settings of the grids and particles are taken from "Introduction to Computational Plasma Physics"(ISBN: 9787030563675)
+
+import taichi as ti
+
+ti.init(arch=ti.gpu)  # Try to run on GPU
+PI = 3.141592653589793
+L = 8 * PI  # simulation domain size
+dt = 0.1  # time step
+substepping = 8
+ng = 32  # number of grids
+np = 16384  # numer of particles
+vb = 1.0  # beam-velocity, one is vb, the other is -vb
+vt = 0.3  # thermal velocity
+wp = 1  # Plasma frequence
+qm = -1  # charge-mass ratio
+q = wp * wp / (qm * np / L)  # charge of a particle
+rho_back = -q * np / L  # background charge density
+dx = L / ng  # grid spacing
+inv_dx = 1.0 / dx
+x = ti.Vector.field(1, ti.f32, np)  # position
+v = ti.Vector.field(1, ti.f32, np)  # velocity
+rho = ti.Vector.field(1, ti.f32, ng)  # charge density
+e = ti.Vector.field(1, ti.f32, ng)  # electric fields
+# to show x-vx on the screen
+v_x_pos1 = ti.Vector.field(2, ti.f32, int(np / 2))
+v_x_pos2 = ti.Vector.field(2, ti.f32, int(np / 2))
+
+
+@ti.kernel
+def initialize():
+    for p in x:
+        x[p].x = (p + 1) * L / np
+        v[p].x = vt * ti.randn() + (-1)**p * vb  # two streams
+
+
+@ti.kernel
+def substep():
+    for p in x:
+        x[p] += v[p] * dt
+        if x[p].x >= L:  # periodic boundary condition
+            x[p] += -L
+        if x[p].x < 0:
+            x[p] += L
+    rho.fill(rho_back)  # fill rho with background charge density
+    for p in x:  # Particle state update and scatter to grid (P2G)
+        base = (x[p] * inv_dx - 0.5).cast(int)
+        fx = x[p] * inv_dx - 0.5 - base.cast(float)
+        rho[base] += (1.0 - fx) * q * inv_dx
+        rho[base + 1] += fx * q * inv_dx
+    e.fill(0.0)
+    ti.loop_config(serialize=True)
+    for i in range(ng):  # compute electric fields
+        e[i] = e[i - 1] + (rho[i - 1] + rho[i]) * dx * 0.5
+    s = 0.0
+    for i in e:
+        s += e[i].x
+    for i in e:
+        e[i] += -s / ng
+    for p in v:  #G2P
+        base = (x[p] * inv_dx - 0.5).cast(int)
+        fx = x[p] * inv_dx - 0.5 - base.cast(float)
+        a = (e[base] *
+             (1.0 - fx) + e[base + 1] * fx) * qm  # compute electric force
+        v[p] += a * dt
+
+
+@ti.kernel
+def vx_pos():  # to show x-vx on the screen
+    for p in x:
+        if p % 2:
+            v_x_pos1[int((p - 1) / 2)].x = x[p].x / L
+            v_x_pos1[int((p - 1) / 2)].y = (v[p].x) / 10 + 0.5
+        else:
+            v_x_pos2[int(p / 2)].x = x[p].x / L
+            v_x_pos2[int(p / 2)].y = (v[p].x) / 10 + 0.5
+
+
+def main():
+    initialize()
+    gui = ti.GUI("Shortest PIC", (800, 800))
+    while not gui.get_event(ti.GUI.ESCAPE, ti.GUI.EXIT):
+        for s in range(substepping):
+            substep()
+        vx_pos()
+        gui.circles(v_x_pos1.to_numpy(), color=0x0000ff, radius=2)
+        gui.circles(v_x_pos2.to_numpy(), color=0xff0000, radius=2)
+        gui.show()
+
+
+if __name__ == '__main__':
+    main()