ViscousGlacier2D

Concise CPU and GPU iterative Stokes solvers for viscous flow - 2D glacier examples.

Description

This repository contains GPU and CPU implementations of a 2D Stokes solver to resolve glacier flow on an inclined plane with a stress-free surface. The routines exemplify the implementation of a fast and concise (60 lines of code) iterative solving strategy referred to as Pseudo-Transient. The core of the Pseudo-Transient approach relies in using physics-motivated transient terms within differential equations in order to iteratively converge to an accurate solution.

The routines relate to a seminar on "Simply solving PDEs". The seminar presentation is accessible here. Further material relating to the pseudo-transient method and pseudo-transient solvers can be found here.

Content

• Script list
• Usage
• Output
• Questions and comments
• Seminar presentation

Script list

The /scripts folder contains the following PT routines:

• viscous_gl2D.jl
• viscous_gl2D_gpu.jl
• viscous_gl2D_nondim.jl
• viscous_gl2D_nondim_gpu.jl

The keywords in the code naming stand for:

• gpu: Nvidia GPU ready routines using the CUDA.jl package
• nondim: non-dimensional version of the code, using natural scaling

Usage

The routines are written in Julia and can be executed from the REPL. Output is produced using PyPlot.jl requiring a valid and on PATH python (+ matplotlib) install.

Example running the viscous_gl2D_nondim.jl routine.

1. Launch Julia

% julia --project

2. ENter package mode ] and instantiate the environment

               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.5.0 (2020-08-01)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia>

(ViscousGlacier2D) pkg> activate .

(ViscousGlacier2D) pkg> instantiate

(ViscousGlacier2D) pkg> st
Status `~/Documents/git/github/ViscousGlacier2D/Project.toml`
  [d330b81b] PyPlot v2.9.0

(ViscousGlacier2D) pkg> 

julia> 

3. Run the script

julia> include("scripts/viscous_gl2D_nondim.jl")
error = 0.007844763087162187
error = 0.0035814871757943543
error = 0.0005235773871451197
error = 6.932325914314143e-5
error = 2.3742721434622532e-5
error = 9.103473750402527e-7
error = 7.903400522027475e-7
error = 7.196251086591826e-8
error = 1.9440634300592754e-8
error = 4.161439365592243e-9
error = 2.54854535939787e-10
error = 1.6094254786093418e-10

julia> 

Output

The output of running the viscous_gl2D_nondim.jl script is following

Questions and comments

Contact me or open an issue if you have any questions or comments about the presented material.

Seminar presentation