examples: add an Lattice Boltzmann Method simulation (#888) (#899)

Co-authored-by: Bruno-Vdr <bruno@asterope.fr>

examples/lbm/cell.v

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+module main
+
+import math
+import rand
+
+// This file contains Code and data structures for a Lattice-Boltzmann-Method (LBM)
+// fluid flow simulation. The simulation is 2 Dimension, with 9 possible directions (D2Q9)
+//
+//  8     1     2
+//
+//  7     0     3
+//
+//  6     5     4
+
+// Vi is an enum for direction vector of D2Q9 Lattice.
+pub enum Vi {
+	center     = 0
+	north      = 1
+	north_east = 2
+	//
+	east       = 3
+	south_east = 4
+	south      = 5
+	//
+	south_west = 6
+	west       = 7
+	north_west = 8
+}
+
+// vfmt off
+const opp = [
+	Vi.center,          Vi.south,      Vi.south_west, 
+	Vi.west,            Vi.north_west, Vi.north, 
+	Vi.north_east, 	    Vi.east,       Vi.south_east,
+]!
+
+// Array defined here in order to loop over a Vi enum.
+// Warning: This array must be coherent with Vi enum order !
+const vi = [
+	Vi.center,          Vi.north,      Vi.north_east,
+	Vi.east,            Vi.south_east, Vi.south, 
+	Vi.south_west,      Vi.west,       Vi.north_west,
+]!
+
+// wi is the weight of mini-cells.
+// Warning: This array must be coherent with Vi enum order !
+const wi = [
+	f64(16.0 / 36.0),   4.0 / 36.0,    1.0 / 36.0, 
+	4.0 / 36.0,         1.0 / 36.0,    4.0 / 36.0, 
+	1.0 / 36.0,         4.0 / 36.0,    1.0 / 36.0,
+]!
+// vfmt on
+
+// opposite returns vector of opposite direction. Yes Enum can have methods in V.
+// Warning: This array must be coherent with Vi enum order !
+fn (v Vi) opposite() Vi {
+	return opp[int(v)]
+}
+
+// Discrete velocity vectors, by component, with respect to SDL display orientation (North is negative on y axis)
+// f64 and int are provided to avoid unnecessary casts.
+// Warning: These vectors must be coherent with Vi enum order !
+const dvx_f = [0.0, 0.0, 1.0, 1.0, 1.0, 0.0, -1.0, -1.0, -1.0]!
+const dvy_f = [0.0, -1.0, -1.0, 0.0, 1.0, 1.0, 1.0, 0.0, -1.0]!
+const dvx_i = [0, 0, 1, 1, 1, 0, -1, -1, -1]!
+const dvy_i = [0, -1, -1, 0, 1, 1, 1, 0, -1]!
+
+struct Cell {
+mut:
+	obstacle bool
+	sp       [9]f64
+}
+
+// Cell.new built, and initializes a default Cell.
+// Warning: sp values must be coherent with Vi enum order !
+fn Cell.new(o bool) Cell {
+	return Cell{
+		obstacle: o
+		sp:       [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]!
+	} // ! means fixed size array ! Will change a day !
+}
+
+// Return a Cell with all mini-cell set to Zero
+fn Cell.zero(o bool) Cell {
+	return Cell{
+		obstacle: o
+		sp:       [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]!
+	}
+}
+
+// normalize perform a normalisation on the cell so that average desnsity is rho0
+fn (mut c Cell) normalize() {
+	rho := c.rho()
+	for mut v in c.sp {
+		v *= (rho0 / rho)
+	}
+}
+
+// randomize add some randomness on the cell.
+fn (mut c Cell) randomize(i f64) {
+	for v in vi {
+		r := rand.f64() * i
+		c.sum(v, r)
+	}
+}
+
+// get returns mini-cell depending on the given speed vector.
+fn (c &Cell) get(v Vi) f64 {
+	return c.sp[int(v)]
+}
+
+// set forces a mini-cell value given its speed vector.
+fn (mut c Cell) set(v Vi, value f64) {
+	c.sp[int(v)] = value
+}
+
+// increase (add value) to a mini-cell value given its speed vector.
+fn (mut c Cell) sum(v Vi, value f64) {
+	c.sp[int(v)] += value
+}
+
+// rho computes whole cell's density
+fn (c &Cell) rho() f64 {
+	mut sum := 0.0
+	for v in c.sp {
+		sum += v
+	}
+	assert math.is_nan(sum) == false
+	return sum
+}
+
+// ux computes x (horizontal) component of cell speed vector.
+fn (c &Cell) ux() f64 {
+	rho := c.rho()
+	r := 1.0 / rho * (c.sp[Vi.north_east] + c.sp[Vi.east] + c.sp[Vi.south_east] - c.sp[Vi.south_west] - c.sp[Vi.west] - c.sp[Vi.north_west])
+	assert math.is_nan(r) == false
+	return r
+}
+
+// uy computes y (vertical) component of cell speed vector.
+fn (c &Cell) uy() f64 {
+	rho := c.rho()
+	r := 1.0 / rho * (-c.sp[Vi.north] - c.sp[Vi.north_east] - c.sp[Vi.north_west] +
+		c.sp[Vi.south_east] + c.sp[Vi.south] + c.sp[Vi.south_west])
+	assert math.is_nan(r) == false
+	return r
+}
+
+// ux_no_rho computes x (horizontal) component of cell speed vector, when rho is already known and passed as param.
+fn (c &Cell) ux_no_rho(rho f64) f64 {
+	r := 1.0 / rho * (c.sp[Vi.north_east] + c.sp[Vi.east] + c.sp[Vi.south_east] - c.sp[Vi.south_west] - c.sp[Vi.west] - c.sp[Vi.north_west])
+	return r
+}
+
+// uy_no_rho computes y (vertical) component of cell speed vector, when rho is already known and passed as param.
+fn (c &Cell) uy_no_rho(rho f64) f64 {
+	r := 1.0 / rho * (-c.sp[Vi.north] - c.sp[Vi.north_east] - c.sp[Vi.north_west] +
+		c.sp[Vi.south_east] + c.sp[Vi.south] + c.sp[Vi.south_west])
+	return r
+}
+
+// equ computes result of equilibrium function.
+fn (c &Cell) equ(i Vi) f64 {
+	rho := c.rho()
+	ux := c.ux_no_rho(rho)
+	uy := c.uy_no_rho(rho)
+
+	t1 := 3.0 * (ux * dvx_f[i] + uy * dvy_f[i])
+	mut t2 := (ux * dvx_f[i] + uy * dvy_f[i])
+
+	t2 *= t2 // t2^2
+	t2 *= (9.0 / 2.0)
+	t3 := (3.0 / 2.0) * (ux * ux + uy * uy)
+	r := wi[i] * rho * (1.0 + t1 + t2 - t3)
+	return r
+}

examples/lbm/colormap.v

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+module main
+
+import arrays
+
+struct Colormap {}
+
+// build a linear color map ARGB8888 from color c1 to c2, of steps colors
+pub fn Colormap.build(c1 u32, c2 u32, steps int) []u32 {
+	assert steps > 1, 'Error, generating colormap needs at least two steps.'
+	mut cm := []u32{cap: steps}
+
+	// split c1 & c2 to RGB channels.
+	mut c1_r := f64((c1 & 0xFF0000) >> 16)
+	mut c1_g := f64((c1 & 0xFF00) >> 8)
+	mut c1_b := f64((c1 & 0xFF))
+
+	c2_r := f64((c2 & 0xFF0000) >> 16)
+	c2_g := f64((c2 & 0xFF00) >> 8)
+	c2_b := f64((c2 & 0xFF))
+
+	delta_r := (c2_r - c1_r) / f64(steps - 1)
+	delta_g := (c2_g - c1_g) / f64(steps - 1)
+	delta_b := (c2_b - c1_b) / f64(steps - 1)
+
+	cm << (0xFF000000 | c1) // Emit exact start color.
+	for _ in 1 .. steps - 1 {
+		c1_r += delta_r
+		c1_g += delta_g
+		c1_b += delta_b
+
+		// Recompose 3 channels to ARGB8888 color.
+		mut c := u32(0xFF_00_00_00)
+		c |= u32(c1_r) << 16
+		c |= u32(c1_g) << 8
+		c |= u32(c1_b)
+		cm << c
+	}
+	cm << (0xFF000000 | c2) // Emit exact end color.
+	return cm
+}
+
+// dual creates a color map with start color, intermediate color and final color, equaly sized.
+fn Colormap.dual(c1 u32, c2 u32, c3 u32, steps int) []u32 {
+	assert steps > 2, 'Error, generating dual-colormap needs at least three steps.'
+	return arrays.append(Colormap.build(c1, c2, steps / 2), Colormap.build(c2, c3, steps - (steps / 2)))
+}