commit 4def6527e85a80d0dc2b52f51aa376c782d296d4
parent f65899ee85de5ed0234d7b2164c22ff80b25a978
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Thu, 4 Apr 2019 16:29:15 +0200
Add working script
Diffstat:
| M | 1d_fd_simple_shear.jl | | | 94 | ++++++++++++++++++++++++++++++++++++++++++++++++++----------------------------- |
1 file changed, 60 insertions(+), 34 deletions(-)
diff --git a/1d_fd_simple_shear.jl b/1d_fd_simple_shear.jl
@@ -9,13 +9,14 @@ import PyPlot
const G = 9.81
## Wall parameters
-const P_wall = 10.0e3 # normal stress [Pa]
+const P_wall = 1.0e3 # normal stress [Pa]
# const v_x_wall = 1e-0 # wall velocity along x [m/s]
const v_x_bot = 0.0 # bottom velocity along x [m/s]
-const μ_wall = 0.382 # stress ratio at top wall
+#const μ_wall = 0.392 # stress ratio at top wall
+const μ_wall = 0.52 # stress ratio at top wall
## Nodes along z
-const nz = 10
+const nz = 100
## Material properties
const A = 0.48 # nonlocal amplitude [-]
@@ -71,22 +72,22 @@ function g_set_bc_neumann(g_ghost)
end
## Compute shear stress from velocity gradient using finite differences
-function shear_stress(v, Δz)
- τ = zero(v)
-
- # compute inner values with central differences
- for i=2:length(v)-1
- τ[i] = (v[i+1] - v[i-1])/(2.0*Δz)
- end
-
- # use forward/backward finite differences at edges
- τ[1] = (v[2] - v[1])/Δz
- τ[end] = (v[end] - v[end-1])/Δz
-
- return τ
-end
+# function shear_stress(v, Δz)
+# τ = zero(v)
+#
+# # compute inner values with central differences
+# for i=2:length(v)-1
+# τ[i] = (v[i+1] - v[i-1])/(2.0*Δz)
+# end
+#
+# # use forward/backward finite differences at edges
+# τ[1] = (v[2] - v[1])/Δz
+# τ[end] = (v[end] - v[end-1])/Δz
+#
+# return τ
+# end
-friction(τ, p) = τ./(p .+ 1e-16)
+#friction(τ, p) = τ./(p .+ 1e-16)
## Fluidity
#fluidity(p, μ, g) = 1.0./(ξ.(μ).^2.0) .* (g .- g_local.(p, μ))
@@ -102,38 +103,57 @@ friction(τ, p) = τ./(p .+ 1e-16)
## A single iteration for solving a Poisson equation Laplace(phi) = f on a
## Cartesian grid. The function returns the normalized residual value
-# TODO f is not used?
-function poisson_solver_1d_iteration(g_in, g_out, μ, p, i, Δz)
+function poisson_solver_1d_iteration(g_in, g_out, μ, p, i, Δz, verbose=false)
coorp_term = Δz^2.0/(2.0*ξ(μ[i])^2.0)
- g_out[i] = 1.0/(1.0 + coorp_term) * (coorp_term*g_local(p[i], μ[i])
- + g_in[i+1]/2.0 + g_in[i-1]/2.0)
-
- return (g_out[i] - g_in[i])^2.0 / (g_out[i]^2.0 + 1e-16)
+ g_local_ = g_local(p[i], μ[i])
+ g_out[i+1] = 1.0/(1.0 + coorp_term) * (coorp_term*g_local(p[i], μ[i])
+ + g_in[i+1+1]/2.0 + g_in[i-1+1]/2.0)
+ res_norm = (g_out[i+1] - g_in[i+1])^2.0 / (g_out[i+1]^2.0 + 1e-16)
+
+ if verbose
+ println("-- $i -----------------")
+ println("coorp_term: $coorp_term")
+ println(" g_local: $g_local_")
+ println(" g_in: $(g_in[i+1])")
+ println(" g_out: $(g_out[i+1])")
+ println(" res_norm: $res_norm")
+ end
+ return res_norm
end
## Iteratively solve the system laplace(phi) = f
function implicit_1d_jacobian_poisson_solver(g, p, μ, Δz,
- rel_tol=1e-4,
+ rel_tol=1e-5,
#max_iter=10_000,
max_iter=10,
- verbose=true)
+ verbose=false)
# allocate second array of g for Jacobian solution procedure
g_out = g
- # transfer ghost node values
- g_out[1] = g[1]
- g_out[end] = g[end]
+ if verbose
+ println("g: ")
+ println(g)
+ println()
+ println("g_out: ")
+ println(g_out)
+ end
# array of normalized residuals
local r_norm = zero(g)
for iter=1:max_iter
+ g_set_bc_neumann(g)
+ if verbose
+ println("g after BC: ")
+ println(g)
+ end
+
# perform a single jacobi iteration in each cell
# if iter%2 == 0
- for iz=2:length(g)-2
+ for iz=1:length(p)
r_norm[iz] = poisson_solver_1d_iteration(g, g_out, μ, p, iz, Δz)
end
# else # reverse direction every second time
@@ -142,9 +162,17 @@ function implicit_1d_jacobian_poisson_solver(g, p, μ, Δz,
# f, iz, Δz)
# end
# end
-
r_norm_max = maximum(r_norm)
+ if verbose
+ println("g after jacobi iteration $iter: ")
+ println(g)
+ println("r_norm:")
+ println(r_norm)
+ println("r_norm_max:")
+ println(r_norm_max)
+ end
+
# Flip-flop arrays
tmp = g
g = g_out
@@ -187,13 +215,11 @@ v_x[1] = v_x_bot
## Calculate stressses
p = p_lithostatic(P_wall, z)
μ = init_μ(μ_wall, ϕ, ρ_s, G, z, P_wall)
-τ = shear_stress(v_x, Δz)
+#τ = shear_stress(v_x, Δz)
#f = forcing(p, μ, g_ghost)
#g_ghost[2:end-1] = f
-g_set_bc_neumann(g_ghost)
-
implicit_1d_jacobian_poisson_solver(g_ghost, p, μ, Δz)
v_x = γ_dot_p(g_ghost[2:end-1], μ)
