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Add baseline and eta_vep-based script.
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| # Initialisation | ||
| using Plots, Printf, Statistics, LinearAlgebra | ||
| Dat = Float64 # Precision (double=Float64 or single=Float32) | ||
| # Macros | ||
| @views av(A) = 0.25*(A[1:end-1,1:end-1].+A[2:end,1:end-1].+A[1:end-1,2:end].+A[2:end,2:end]) | ||
| @views av_xa(A) = 0.5*(A[1:end-1,:].+A[2:end,:]) | ||
| @views av_ya(A) = 0.5*(A[:,1:end-1].+A[:,2:end]) | ||
| # 2D Stokes routine | ||
| @views function Stokes2D_vep() | ||
| do_DP = true # do_DP=false: Von Mises, do_DP=true: Drucker-Prager (friction angle) | ||
| η_reg = 1.2e-2 # regularisation "viscosity" | ||
| # Physics | ||
| Lx, Ly = 1.0, 1.0 # domain size | ||
| radi = 0.01 # inclusion radius | ||
| τ_y = 1.6 # yield stress. If do_DP=true, τ_y stand for the cohesion: c*cos(ϕ) | ||
| sinϕ = sind(30)*do_DP # sinus of the friction angle | ||
| μ0 = 1.0 # viscous viscosity | ||
| G0 = 1.0 # elastic shear modulus | ||
| Gi = G0/(6.0-4.0*do_DP) # elastic shear modulus perturbation | ||
| εbg = 1.0 # background strain-rate | ||
| # Numerics | ||
| nt = 10 # number of time steps | ||
| nx, ny = 63, 63 # numerical grid resolution | ||
| Vdmp = 4.0 # convergence acceleration (damping) | ||
| Vsc = 2.0 # iterative time step limiter | ||
| Ptsc = 6.0 # iterative time step limiter | ||
| ε = 1e-6 # nonlinear tolerence | ||
| iterMax = 3e4 # max number of iters | ||
| nout = 200 # check frequency | ||
| # Preprocessing | ||
| dx, dy = Lx/nx, Ly/ny | ||
| dt = μ0/G0/4.0 # assumes Maxwell time of 4 | ||
| # Array initialisation | ||
| Pt = zeros(Dat, nx ,ny ) | ||
| ∇V = zeros(Dat, nx ,ny ) | ||
| Vx = zeros(Dat, nx+1,ny ) | ||
| Vy = zeros(Dat, nx ,ny+1) | ||
| Exx = zeros(Dat, nx ,ny ) | ||
| Eyy = zeros(Dat, nx ,ny ) | ||
| Exyv = zeros(Dat, nx+1,ny+1) | ||
| Exx1 = zeros(Dat, nx ,ny ) | ||
| Eyy1 = zeros(Dat, nx ,ny ) | ||
| Exy1 = zeros(Dat, nx ,ny ) | ||
| Exyv1 = zeros(Dat, nx+1,ny+1) | ||
| Txx = zeros(Dat, nx ,ny ) | ||
| Tyy = zeros(Dat, nx ,ny ) | ||
| Txy = zeros(Dat, nx ,ny ) | ||
| Txyv = zeros(Dat, nx+1,ny+1) | ||
| Txx_o = zeros(Dat, nx ,ny ) | ||
| Tyy_o = zeros(Dat, nx ,ny ) | ||
| Txy_o = zeros(Dat, nx ,ny ) | ||
| Txyv_o = zeros(Dat, nx+1,ny+1) | ||
| Tii = zeros(Dat, nx ,ny ) | ||
| Eii = zeros(Dat, nx ,ny ) | ||
| F = zeros(Dat, nx ,ny ) | ||
| Fchk = zeros(Dat, nx ,ny ) | ||
| Pla = zeros(Dat, nx ,ny ) | ||
| λ = zeros(Dat, nx ,ny ) | ||
| dQdTxx = zeros(Dat, nx ,ny ) | ||
| dQdTyy = zeros(Dat, nx ,ny ) | ||
| dQdTxy = zeros(Dat, nx ,ny ) | ||
| Rx = zeros(Dat, nx-1,ny ) | ||
| Ry = zeros(Dat, nx ,ny-1) | ||
| dVxdt = zeros(Dat, nx-1,ny ) | ||
| dVydt = zeros(Dat, nx ,ny-1) | ||
| dtPt = zeros(Dat, nx ,ny ) | ||
| dtVx = zeros(Dat, nx-1,ny ) | ||
| dtVy = zeros(Dat, nx ,ny-1) | ||
| Rog = zeros(Dat, nx ,ny ) | ||
| η_v = μ0*ones(Dat, nx, ny) | ||
| η_e = dt*G0*ones(Dat, nx, ny) | ||
| η_ev = dt*G0*ones(Dat, nx+1, ny+1) | ||
| η_ve = ones(Dat, nx, ny) | ||
| η_vep = ones(Dat, nx, ny) | ||
| η_vepv = ones(Dat, nx+1, ny+1) | ||
| # Initial condition | ||
| xc, yc = LinRange(dx/2, Lx-dx/2, nx), LinRange(dy/2, Ly-dy/2, ny) | ||
| xc, yc = LinRange(dx/2, Lx-dx/2, nx), LinRange(dy/2, Ly-dy/2, ny) | ||
| xv, yv = LinRange(0.0, Lx, nx+1), LinRange(0.0, Ly, ny+1) | ||
| (Xvx,Yvx) = ([x for x=xv,y=yc], [y for x=xv,y=yc]) | ||
| (Xvy,Yvy) = ([x for x=xc,y=yv], [y for x=xc,y=yv]) | ||
| radc = (xc.-Lx./2).^2 .+ (yc'.-Ly./2).^2 | ||
| radv = (xv.-Lx./2).^2 .+ (yv'.-Ly./2).^2 | ||
| η_e[radc.<radi] .= dt*Gi | ||
| η_ev[radv.<radi].= dt*Gi | ||
| η_ve .= (1.0./η_e + 1.0./η_v).^-1 | ||
| Vx .= εbg.*Xvx | ||
| Vy .= .-εbg.*Yvy | ||
| # Time loop | ||
| t=0.0; evo_t=[]; evo_Txx=[]; niter = 0 | ||
| for it = 1:nt | ||
| iter=1; err=2*ε; err_evo1=[]; err_evo2=[] | ||
| Txx_o.=Txx; Tyy_o.=Tyy; Txy_o.=av(Txyv); Txyv_o.=Txyv; λ.=0.0 | ||
| local itg | ||
| while (err>ε && iter<=iterMax) | ||
| # divergence - pressure | ||
| ∇V .= diff(Vx, dims=1)./dx .+ diff(Vy, dims=2)./dy | ||
| Pt .= Pt .- dtPt.*∇V | ||
| # strain rates | ||
| Exx .= diff(Vx, dims=1)./dx .- 1.0/3.0*∇V | ||
| Eyy .= diff(Vy, dims=2)./dy .- 1.0/3.0*∇V | ||
| Exyv[2:end-1,2:end-1] .= 0.5.*(diff(Vx[2:end-1,:], dims=2)./dy .+ diff(Vy[:,2:end-1], dims=1)./dx) | ||
| # visco-elastic strain rates | ||
| Exx1 .= Exx .+ Txx_o ./2.0./η_e | ||
| Eyy1 .= Eyy .+ Tyy_o ./2.0./η_e | ||
| Exyv1 .= Exyv .+ Txyv_o./2.0./η_ev | ||
| Exy1 .= av(Exyv) .+ Txy_o ./2.0./η_e | ||
| Eii .= sqrt.(0.5*(Exx1.^2 .+ Eyy1.^2) .+ Exy1.^2) | ||
| # trial stress | ||
| Txx .= 2.0.*η_ve.*Exx1 | ||
| Tyy .= 2.0.*η_ve.*Eyy1 | ||
| Txy .= 2.0.*η_ve.*Exy1 | ||
| Tii .= sqrt.(0.5*(Txx.^2 .+ Tyy.^2) .+ Txy.^2) | ||
| # yield function | ||
| F .= Tii .- τ_y .- Pt.*sinϕ | ||
| Pla .= 0.0 | ||
| Pla .= F .> 0.0 | ||
| λ .= Pla.*F./(η_ve .+ η_reg) | ||
| dQdTxx .= 0.5.*Txx./Tii | ||
| dQdTyy .= 0.5.*Tyy./Tii | ||
| dQdTxy .= Txy./Tii | ||
| # plastic corrections | ||
| Txx .= 2.0.*η_ve.*(Exx1 .- λ.*dQdTxx) | ||
| Tyy .= 2.0.*η_ve.*(Eyy1 .- λ.*dQdTyy) | ||
| Txy .= 2.0.*η_ve.*(Exy1 .- 0.5.*λ.*dQdTxy) | ||
| Tii .= sqrt.(0.5*(Txx.^2 .+ Tyy.^2) .+ Txy.^2) | ||
| Fchk .= Tii .- τ_y .- Pt.*sinϕ .- λ.*η_reg | ||
| η_vep .= Tii./2.0./Eii | ||
| η_vepv[2:end-1,2:end-1] .= av(η_vep); η_vepv[1,:].=η_vepv[2,:]; η_vepv[end,:].=η_vepv[end-1,:]; η_vepv[:,1].=η_vepv[:,2]; η_vepv[:,end].=η_vepv[:,end-1] | ||
| Txyv .= 2.0.*η_vepv.*Exyv1 | ||
| # PT timestep | ||
| dtVx .= min(dx,dy)^2.0./av_xa(η_vep)./4.1./Vsc | ||
| dtVy .= min(dx,dy)^2.0./av_ya(η_vep)./4.1./Vsc | ||
| dtPt .= 4.1.*η_vep./max(nx,ny)./Ptsc | ||
| # velocities | ||
| Rx .= .-diff(Pt, dims=1)./dx .+ diff(Txx, dims=1)./dx .+ diff(Txyv[2:end-1,:], dims=2)./dy | ||
| Ry .= .-diff(Pt, dims=2)./dy .+ diff(Tyy, dims=2)./dy .+ diff(Txyv[:,2:end-1], dims=1)./dx .+ av_ya(Rog) | ||
| dVxdt .= dVxdt.*(1-Vdmp/nx) .+ Rx | ||
| dVydt .= dVydt.*(1-Vdmp/ny) .+ Ry | ||
| Vx[2:end-1,:] .= Vx[2:end-1,:] .+ dVxdt.*dtVx | ||
| Vy[:,2:end-1] .= Vy[:,2:end-1] .+ dVydt.*dtVy | ||
| # convergence check | ||
| if mod(iter, nout)==0 | ||
| norm_Rx = norm(Rx)/sqrt(length(Rx)); norm_Ry = norm(Ry)/sqrt(length(Ry)); norm_∇V = norm(∇V)/sqrt(length(∇V)) | ||
| err = maximum([norm_Rx, norm_Ry, norm_∇V]) | ||
| push!(err_evo1, err); push!(err_evo2, itg) | ||
| @printf("it = %d, iter = %d, err = %1.2e norm[Rx=%1.2e, Ry=%1.2e, ∇V=%1.2e] (Fchk=%1.2e) \n", it, itg, err, norm_Rx, norm_Ry, norm_∇V, maximum(Fchk)) | ||
| end | ||
| iter+=1; itg=iter; niter += 1 | ||
| end | ||
| t = t + dt | ||
| push!(evo_t, t); push!(evo_Txx, maximum(Txx)) | ||
| # Plotting | ||
| p1 = heatmap(xv, yc, Vx' , aspect_ratio=1, xlims=(0, Lx), ylims=(dy/2, Ly-dy/2), c=:inferno, title="Vx") | ||
| # p2 = heatmap(xc, yv, Vy' , aspect_ratio=1, xlims=(dx/2, Lx-dx/2), ylims=(0, Ly), c=:inferno, title="Vy") | ||
| p2 = heatmap(xc, yc, η_vep' , aspect_ratio=1, xlims=(dx/2, Lx-dx/2), ylims=(0, Ly), c=:inferno, title="η_vep") | ||
| p3 = heatmap(xc, yc, Tii' , aspect_ratio=1, xlims=(dx/2, Lx-dx/2), ylims=(0, Ly), c=:inferno, title="τii") | ||
| p4 = plot(evo_t, evo_Txx , legend=false, xlabel="time", ylabel="max(τxx)", linewidth=0, markershape=:circle, framestyle=:box, markersize=3) | ||
| plot!(evo_t, 2.0.*εbg.*μ0.*(1.0.-exp.(.-evo_t.*G0./μ0)), linewidth=2.0) # analytical solution for VE loading | ||
| plot!(evo_t, 2.0.*εbg.*μ0.*ones(size(evo_t)), linewidth=2.0) # viscous flow stress | ||
| if !do_DP plot!(evo_t, τ_y*ones(size(evo_t)), linewidth=2.0) end # von Mises yield stress | ||
| display(plot(p1, p2, p3, p4)) | ||
| end | ||
| println(niter) | ||
| return | ||
| end | ||
|
|
||
| Stokes2D_vep() |
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| using Plots,LinearAlgebra,Printf | ||
| # helper functions | ||
| @views av(A) = 0.25*(A[1:end-1,1:end-1].+A[2:end,1:end-1].+A[1:end-1,2:end].+A[2:end,2:end]) | ||
| @views av_xa(A) = 0.5*(A[1:end-1,:].+A[2:end,:]) | ||
| @views av_ya(A) = 0.5*(A[:,1:end-1].+A[:,2:end]) | ||
| @views maxloc(A) = max.(A[1:end-2,1:end-2],A[1:end-2,2:end-1],A[1:end-2,3:end], | ||
| A[2:end-1,1:end-2],A[2:end-1,2:end-1],A[2:end-1,3:end], | ||
| A[3:end ,1:end-2],A[3:end ,2:end-1],A[3:end ,3:end]) | ||
| @views bc2!(A) = begin A[1,:] = A[2,:]; A[end,:] = A[end-1,:]; A[:,1] = A[:,2]; A[:,end] = A[:,end-1] end | ||
| # main function | ||
| @views function Stokes2D_vep() | ||
| use_vep = true | ||
| # phyiscs | ||
| lx,ly = 1.0,1.0 | ||
| radi = 0.1 | ||
| η0 = 1.0 | ||
| η_reg = 1.2e-2 | ||
| G0 = 1.0 | ||
| Gi = 0.5G0 | ||
| τ_y = 1.6 | ||
| sinϕ = sind(30) | ||
| ebg = 1.0 | ||
| dt = η0/G0/4.0 | ||
| # numerics | ||
| nx,ny = 63,63 | ||
| nt = 10 | ||
| εnl = 1e-6 | ||
| maxiter = 150max(nx,ny) | ||
| nchk = 2max(nx,ny) | ||
| Re = 5π | ||
| r = 1.0 | ||
| CFL = 0.99/sqrt(2) | ||
| # preprocessing | ||
| dx,dy = lx/nx,ly/ny | ||
| max_lxy = max(lx,ly) | ||
| vpdτ = CFL*min(dx,dy) | ||
| xc,yc = LinRange(-(lx-dx)/2,(lx-dx)/2,nx),LinRange(-(ly-dy)/2,(ly-dy)/2,ny) | ||
| xv,yv = LinRange(-lx/2,lx/2,nx+1),LinRange(-ly/2,ly/2,ny+1) | ||
| # allocate arrays | ||
| Pr = zeros(nx ,ny ) | ||
| τxx = zeros(nx ,ny ) | ||
| τyy = zeros(nx ,ny ) | ||
| τxy = zeros(nx+1,ny+1) | ||
| τxyc = zeros(nx ,ny ) | ||
| τii = zeros(nx ,ny ) | ||
| Eii = zeros(nx ,ny ) | ||
| λ = zeros(nx ,ny ) | ||
| F = zeros(nx ,ny ) | ||
| Fchk = zeros(nx ,ny ) | ||
| dQdTxx = zeros(nx ,ny ) | ||
| dQdTyy = zeros(nx ,ny ) | ||
| dQdTxy = zeros(nx ,ny ) | ||
| τxx_o = zeros(nx ,ny ) | ||
| τyy_o = zeros(nx ,ny ) | ||
| τxy_o = zeros(nx+1,ny+1) | ||
| Vx = zeros(nx+1,ny ) | ||
| Vy = zeros(nx ,ny+1) | ||
| dVx = zeros(nx-1,ny ) | ||
| dVy = zeros(nx ,ny-1) | ||
| Rx = zeros(nx-1,ny ) | ||
| Ry = zeros(nx ,ny-1) | ||
| ∇V = zeros(nx ,ny ) | ||
| ρg = zeros(nx ,ny ) | ||
| Exx = zeros(nx ,ny ) | ||
| Eyy = zeros(nx ,ny ) | ||
| Exy = zeros(nx+1,ny+1) | ||
| Exx_e = zeros(nx ,ny ) | ||
| Eyy_e = zeros(nx ,ny ) | ||
| Exy_e = zeros(nx+1,ny+1) | ||
| Exx_τ = zeros(nx ,ny ) | ||
| Eyy_τ = zeros(nx ,ny ) | ||
| Exy_τ = zeros(nx+1,ny+1) | ||
| Exyc_τ = zeros(nx ,ny ) | ||
| η_ve_τ = zeros(nx ,ny ) | ||
| η_ve_τv = zeros(nx+1,ny+1) | ||
| η_ve = zeros(nx ,ny ) | ||
| η_vem = zeros(nx ,ny ) | ||
| η_vev = zeros(nx+1,ny+1) | ||
| η_vevm = zeros(nx+1,ny+1) | ||
| dτ_ρ = zeros(nx ,ny ) | ||
| dτ_ρv = zeros(nx+1,ny+1) | ||
| Gdτ = zeros(nx ,ny ) | ||
| Gdτv = zeros(nx+1,ny+1) | ||
| η_vep = zeros(nx ,ny ) | ||
| η_vepv = zeros(nx+1,ny+1) | ||
| # init | ||
| Vx = [ ebg*x for x ∈ xv, _ ∈ yc ] | ||
| Vy = [-ebg*y for _ ∈ xc, y ∈ yv ] | ||
| η = fill(η0,nx,ny); ηv = fill(η0,nx+1,ny+1) | ||
| G = fill(G0,nx,ny); Gv = fill(G0,nx+1,ny+1) | ||
| @. G[xc^2 + yc'^2 < radi^2] = Gi | ||
| @. Gv[xv^2 + yv'^2 < radi^2] = Gi | ||
| η_e = G.*dt; η_ev = Gv.*dt | ||
| @. η_ve = 1.0/(1.0/η + 1.0/η_e) | ||
| @. η_vev = 1.0/(1.0/ηv + 1.0/η_ev) | ||
| @. η_vep = 1.0/(1.0/η + 1.0/η_e) | ||
| @. η_vepv = 1.0/(1.0/ηv + 1.0/η_ev) | ||
| # action | ||
| t = 0.0; evo_t = Float64[]; evo_τxx = Float64[]; niter = 0 | ||
| for it = 1:nt | ||
| τxx_o .= τxx; τyy_o .= τyy; τxy_o .= τxy | ||
| err = 2εnl; iter = 0 | ||
| while err > εnl && iter < maxiter | ||
| if !use_vep | ||
| η_vem[2:end-1,2:end-1] .= maxloc(η_ve) ; bc2!(η_vem) | ||
| η_vevm[2:end-1,2:end-1] .= maxloc(η_vev); bc2!(η_vevm) | ||
| else | ||
| η_vem[2:end-1,2:end-1] .= maxloc(η_vep) ; bc2!(η_vem) | ||
| η_vevm[2:end-1,2:end-1] .= maxloc(η_vepv); bc2!(η_vevm) | ||
| end | ||
| @. dτ_ρ = vpdτ*max_lxy/Re/η_vem | ||
| @. dτ_ρv = vpdτ*max_lxy/Re/η_vevm | ||
| @. Gdτ = vpdτ^2/dτ_ρ/(r+2.0) | ||
| @. Gdτv = vpdτ^2/dτ_ρv/(r+2.0) | ||
| @. η_ve_τ = 1.0/(1.0/η + 1.0/η_e + 1.0/Gdτ) | ||
| @. η_ve_τv = 1.0/(1.0/ηv + 1.0/η_ev + 1.0/Gdτv) | ||
| # pressure | ||
| ∇V .= diff(Vx, dims=1)./dx .+ diff(Vy, dims=2)./dy | ||
| @. Pr -= r*Gdτ*∇V | ||
| # strain rates | ||
| Exx .= diff(Vx, dims=1)./dx | ||
| Eyy .= diff(Vy, dims=2)./dy | ||
| Exy[2:end-1,2:end-1] .= 0.5.*(diff(Vx[2:end-1,:], dims=2)./dy .+ diff(Vy[:,2:end-1], dims=1)./dx) | ||
| # viscoelastic strain rates | ||
| @. Exx_e = Exx + τxx_o/2.0/η_e | ||
| @. Eyy_e = Eyy + τyy_o/2.0/η_e | ||
| @. Exy_e = Exy + τxy_o/2.0/η_ev | ||
| # viscoelastic pseudo-transient strain rates | ||
| @. Exx_τ = Exx_e + τxx/2.0/Gdτ | ||
| @. Eyy_τ = Eyy_e + τyy/2.0/Gdτ | ||
| @. Exy_τ = Exy_e + τxy/2.0/Gdτv | ||
| # stress update | ||
| @. τxx = 2.0*η_ve_τ *Exx_τ | ||
| @. τyy = 2.0*η_ve_τ *Eyy_τ | ||
| @. τxy = 2.0*η_ve_τv*Exy_τ | ||
| @. τxyc = 2.0*η_ve_τ*Exyc_τ | ||
| # stress and strain rate invariants | ||
| @. τii = sqrt(0.5*(τxx^2 + τyy^2) + τxyc*τxyc) | ||
| @. Eii = sqrt(0.5*(Exx_τ^2 + Eyy_τ^2) + Exyc_τ*Exyc_τ) | ||
| # yield function | ||
| @. F = τii - τ_y - Pr.*sinϕ | ||
| @. λ = max(F,0.0)/(η_ve_τ + η_reg) | ||
| @. dQdTxx = 0.5*τxx /τii | ||
| @. dQdTyy = 0.5*τyy /τii | ||
| @. dQdTxy = τxyc/τii | ||
| # plastic correction | ||
| @. τxx = 2.0*η_ve_τ *(Exx_τ - λ*dQdTxx) | ||
| @. τyy = 2.0*η_ve_τ *(Eyy_τ - λ*dQdTyy) | ||
| @. τxyc = 2.0*η_ve_τ *(Exyc_τ - 0.5*λ*dQdTxy) | ||
| τxy[2:end-1,2:end-1] .= 2.0 .* η_ve_τv[2:end-1,2:end-1].*(Exy_τ[2:end-1,2:end-1] .- 0.5 .* av(λ.*dQdTxy)) | ||
| @. τii = sqrt(0.5*(τxx^2 + τyy^2) + τxyc*τxyc) | ||
| @. Fchk = τii - τ_y - Pr*sinϕ - λ*η_reg | ||
| @. η_vep = τii / 2.0 / Eii * 19.3 | ||
| η_vepv[2:end-1,2:end-1] .= av(η_vep); bc2!(η_vep) | ||
| # velocity update | ||
| dVx .= av_xa(dτ_ρ) .* (.-diff(Pr, dims=1)./dx .+ diff(τxx, dims=1)./dx .+ diff(τxy[2:end-1,:], dims=2)./dy) | ||
| dVy .= av_ya(dτ_ρ) .* (.-diff(Pr, dims=2)./dy .+ diff(τyy, dims=2)./dy .+ diff(τxy[:,2:end-1], dims=1)./dx .+ av_ya(ρg)) | ||
| @. Vx[2:end-1,:] = Vx[2:end-1,:] + dVx | ||
| @. Vy[:,2:end-1] = Vy[:,2:end-1] + dVy | ||
| if iter % nchk == 0 | ||
| Rx .= .-diff(Pr, dims=1)./dx .+ diff(τxx, dims=1)./dx .+ diff(τxy[2:end-1,:], dims=2)./dy | ||
| Ry .= .-diff(Pr, dims=2)./dy .+ diff(τyy, dims=2)./dy .+ diff(τxy[:,2:end-1], dims=1)./dx .+ av_ya(ρg) | ||
| norm_Rx = norm(Rx)/sqrt(length(Rx)); norm_Ry = norm(Ry)/sqrt(length(Ry)); norm_∇V = norm(∇V)/sqrt(length(∇V)) | ||
| err = maximum([norm_Rx, norm_Ry, norm_∇V]) | ||
| @printf("it = %d, iter = %d, err = %1.2e norm[Rx=%1.2e, Ry=%1.2e, ∇V=%1.2e] (Fchk=%1.2e) \n", it, iter, err, norm_Rx, norm_Ry, norm_∇V, maximum(Fchk)) | ||
| end | ||
| iter += 1; niter += 1 | ||
| end | ||
| t += dt; push!(evo_t, t); push!(evo_τxx, maximum(τxx)) | ||
| p1 = heatmap(xc,yc,τii',aspect_ratio=1,xlims=(-lx/2,lx/2),ylims=(-ly/2,ly/2),title="τii") | ||
| # p3 = heatmap(xc,yc,η_vep',aspect_ratio=1,xlims=(-lx/2,lx/2),ylims=(-ly/2,ly/2),title="τii") | ||
| p2 = plot(evo_t, evo_τxx , legend=false, xlabel="time", ylabel="max(τxx)", linewidth=0, markershape=:circle, framestyle=:box, markersize=3) | ||
| plot!(evo_t, 2.0.*ebg.*η0.*(1.0.-exp.(.-evo_t.*G0./η0)), linewidth=2.0) # analytical solution for VE loading | ||
| plot!(evo_t, 2.0.*ebg.*η0.*ones(size(evo_t)), linewidth=2.0) # viscous flow stress | ||
| display(plot(p1,p2)) | ||
| end | ||
| println(niter) | ||
| return | ||
| end | ||
| # action | ||
| Stokes2D_vep() |