flownet_geometry_quadrilateral: Define flow net problem using gridded quadrilateral domain...

In GJMeijer/soilmech: R functions and plots for Soil Mechanics teaching

Define flow net problem using gridded quadrilateral domain system

Description

Defines a geometry for a flow net problem. quadrilateral domains are defined using a grid system. For each domain, horizontal and vertical permeabilities may be defined seperately. All quadrilateral domains should be strictly convex in shape.

Domains that are next to each other in the grid are automatically connected. All boundary conditions are assumed impermeable, unless otherwise defined using the inputs 'bc_id', 'bc_edge', 'bc_type' and 'bc_value'.

Defines a geometry for a flow net problem. quadrilateral domains are defined using a grid system. For each domain, horizontal and vertical permeabilities may be defined seperately. All quadrilateral domains should be strictly convex in shape.

Domains that are next to each other in the grid are automatically connected. All boundary conditions are assumed impermeable, unless otherwise defined using the inputs 'bc_id', 'bc_edge', 'bc_type' and 'bc_value'.

Usage

flownet_geometry_quadrilateral(
  x = matrix(c(1, 3, 6, 1, 3, 5, 1, 3, 5), ncol = 3, byrow = FALSE),
  y = matrix(c(0, 0, 0, 1, 1, 1.5, 2.5, 2, 2), ncol = 3, byrow = FALSE),
  ix = c(1, 1, 2),
  iy = c(2, 1, 1),
  kx = 1e-06,
  ky = 1e-06,
  grid_size = 0.05,
  bc_domain = c(1, 3),
  bc_edge = c(2, 3),
  bc_type = c("h", "h"),
  bc_value = c(10, 5),
  node_min = 3
)

flownet_geometry_quadrilateral(
  x = matrix(c(1, 3, 6, 1, 3, 5, 1, 3, 5), ncol = 3, byrow = FALSE),
  y = matrix(c(0, 0, 0, 1, 1, 1.5, 2.5, 2, 2), ncol = 3, byrow = FALSE),
  ix = c(1, 1, 2),
  iy = c(2, 1, 1),
  kx = 1e-06,
  ky = 1e-06,
  grid_size = 0.05,
  bc_domain = c(1, 3),
  bc_edge = c(2, 3),
  bc_type = c("h", "h"),
  bc_value = c(10, 5),
  node_min = 3
)

Arguments

x	matrix of x-coordinates of corner points in domain
y	matrix of y-coordinates of corner points in domain
ix	x-index in grid of soil rectangle (length n)
iy	y-index in grid of soil rectangle (length n)
kx, ky	horizontal and vertical permeabilities. Either define as arrays (with length n), or as scalars if the permeability is the same in each domain
grid_size	the requested grid size. Actual sizes may be slightly larger to ensure a regular number of nodes fits in each domain. Thus grid sizes may be slightly different in each domain
bc_domain	domain at which the boundary condition applies (array with length m, the integers relate to the position in 'ix','iy')
bc_edge	edge in domain at which the boundary condition applies ( array with length m). Edges are numbered clockwise: '1' for left (negative x-face), '2' for top (positive y-face), '3' for right ( positive x-face) or '4' for bottom (negative y-face)
bc_type	type of boundary condition (array with length m). Use 'h' for a known head, and 'q' for a known flow (positive when flowing into the domain)
bc_value	Values for boundary conditions (array with length m). If 'bc_type == "h"', it defines the known hydraulic head on the boundary. If 'bc_type == "q"', it defines the fixed discharge into the domain on this boundary.
node_min	minimum number of nodes in each direction in each domain. Set to at least 3 to ensure finite difference approximation works properly

Examples

flownet_geometry_quadrilateral()
flownet_geometry_quadrilateral()

GJMeijer/soilmech documentation built on May 22, 2022, 10:39 a.m.