Approximating upwind gradients on a grid with the following options for the order of accuracy: 1, 3 or 5.
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#include <cmath>
#include "Grid/grid_dist_id.hpp"
#include "FD_simple.hpp"
#include "Eno_Weno.hpp"
#include "level_set/redistancing_Sussman/HelpFunctions.hpp"
Go to the source code of this file.
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| template<typename field_type > |
| static field_type | upwinding (field_type dplus, field_type dminus, int sign) |
| | Upwinding: For a specific dimension, from the forward and backward gradient find the upwind side.
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| template<typename velocity_type > |
| int | get_sign_velocity (velocity_type v, size_t d) |
| | Returns the sign of a scalar velocity field.
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| template<typename velocity_type > |
| int | get_sign_velocity (velocity_type v[], size_t d) |
| | Returns the sign of one component in a vector velocity field.
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| template<size_t Field, size_t Velocity, typename gridtype , typename keytype > |
| auto | FD_upwind (gridtype &grid, keytype &key, size_t d, size_t order) |
| | Get the upwind finite difference of a scalar property on the current grid node.
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| template<size_t Field, size_t Velocity, size_t Gradient, typename gridtype > |
| void | upwind_gradient (gridtype &grid, const bool one_sided_BC, size_t order) |
| | Computes upwind gradient with order of accuracy 1, 3 or 5.
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| template<typename gridtype > |
| static bool | ghost_width_is_sufficient (gridtype &grid, size_t required_width) |
| | Checks if ghost layer is thick enough for a given stencil-width.
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| template<size_t Field_in, size_t Velocity, size_t Gradient_out, typename gridtype > |
| void | get_upwind_gradient (gridtype &grid, const size_t order=5, const bool one_sided_BC=true) |
| | Calls upwind_gradient. Computes upwind gradient of desired order {1, 3, 5} for the whole n-dim grid.
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Approximating upwind gradients on a grid with the following options for the order of accuracy: 1, 3 or 5.
For solving hyperbolic PDEs using differencing that is biased by the direction of the wave front. Upwinding is done according to M. Sussman and E. Fatemi, “Efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow” (1999) ), paragraph 4.1, 2 b). Order 1 is achieved by upwinding of forward and backward finite difference, order 3 and 5 by upwinding the ENO and WENO scheme, respectively.
- Author
- Justina Stark
- Date
- May 2021
Definition in file Upwind_gradient.hpp.
◆ FD_upwind()
template<size_t Field, size_t Velocity, typename gridtype , typename keytype >
| auto FD_upwind |
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gridtype & |
grid, |
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keytype & |
key, |
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size_t |
d, |
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size_t |
order |
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) |
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Get the upwind finite difference of a scalar property on the current grid node.
Order of accuracy can be 1, 3 or 5.
- Template Parameters
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| Field | Size_t index of property for which the gradient should be computed. |
| Velocity | Size_t index of property that contains the velocity field. Can be scalar or vector field. |
| gridtype | Type of input grid. |
| keytype | Type of key variable. |
- Parameters
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| grid | Grid, on which the gradient should be computed. |
| key | Key that contains the index of the current grid node. |
| d | Variable (size_t) that contains the dimension. |
| order | Order of accuracy of the difference scheme. Can be 1, 3 or 5. |
- Returns
- Upwind finite difference in one dimension of the property under index Field on the current node with index key.
Definition at line 95 of file Upwind_gradient.hpp.
◆ get_sign_velocity() [1/2]
template<typename velocity_type >
| int get_sign_velocity |
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velocity_type |
v, |
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size_t |
d |
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) |
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inline |
Returns the sign of a scalar velocity field.
- Template Parameters
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| velocity_type | Template type of velocity (scalar). |
- Parameters
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| v | Velocity of type velocity_type. |
| d | Dimension. This is a dummy to simplify call in module FD_upwind. |
- Returns
- Sign of velocity v.
Definition at line 62 of file Upwind_gradient.hpp.
◆ get_sign_velocity() [2/2]
template<typename velocity_type >
| int get_sign_velocity |
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velocity_type |
v[], |
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size_t |
d |
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) |
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inline |
Returns the sign of one component in a vector velocity field.
- Template Parameters
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| velocity_type | Template type of velocity (vector). |
- Parameters
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| v | Velocity of type velocity_type. |
| d | Component of velocity vector for which sign should be returned. |
- Returns
- Sign of component d from velocity v.
Definition at line 75 of file Upwind_gradient.hpp.
◆ get_upwind_gradient()
template<size_t Field_in, size_t Velocity, size_t Gradient_out, typename gridtype >
| void get_upwind_gradient |
( |
gridtype & |
grid, |
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const size_t |
order = 5, |
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const bool |
one_sided_BC = true |
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) |
| |
Calls upwind_gradient. Computes upwind gradient of desired order {1, 3, 5} for the whole n-dim grid.
- Template Parameters
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| Field | Size_t index of property for which the gradient should be computed. |
| Velocity | Size_t index of property that contains the velocity field. Can be scalar or vector field. |
| Gradient | Size_t index of property where the upwind gradient result should be stored. |
| gridtype | Type of input grid. |
- Parameters
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| grid | Grid, on which the gradient should be computed. |
Definition at line 242 of file Upwind_gradient.hpp.
◆ ghost_width_is_sufficient()
template<typename gridtype >
| static bool ghost_width_is_sufficient |
( |
gridtype & |
grid, |
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size_t |
required_width |
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) |
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static |
Checks if ghost layer is thick enough for a given stencil-width.
- Template Parameters
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| gridtype | Type of input grid. |
- Parameters
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| grid | Grid, for which ghost layer width should be checked. |
| required_width | Size_t variable, number of ghost nodes that are required in one direction. |
- Returns
- Bool, true if ghost layer sufficiently large, false otherwise.
Definition at line 214 of file Upwind_gradient.hpp.
◆ upwind_gradient()
template<size_t Field, size_t Velocity, size_t Gradient, typename gridtype >
| void upwind_gradient |
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gridtype & |
grid, |
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const bool |
one_sided_BC, |
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size_t |
order |
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) |
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Computes upwind gradient with order of accuracy 1, 3 or 5.
Checks if a point lays within the grid or at the boundary. For the internal grid points, it calls upwind finite difference FD_upwind(). For the border points, simply FD_forward() and FD_backward() is used, respectively, depending on the side of the border.
- Template Parameters
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| Field | Size_t index of property for which the gradient should be computed. |
| Velocity | Size_t index of property that contains the velocity field. Can be scalar or vector field. |
| Gradient | Size_t index of property where the gradient result should be stored. |
| gridtype | Type of input grid. |
- Parameters
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| grid | Grid, on which the gradient should be computed. |
| one_sided_BC | Bool variable, if true, use one-sided kernel for boundary-nodes. If false, extend stencil onto ghost nodes. |
| order | Size_t variable, order of accuracy the upwind FD scheme should have. Can be 1, 3 or 5. |
Definition at line 149 of file Upwind_gradient.hpp.
◆ upwinding()
template<typename field_type >
| static field_type upwinding |
( |
field_type |
dplus, |
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field_type |
dminus, |
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int |
sign |
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) |
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static |
Upwinding: For a specific dimension, from the forward and backward gradient find the upwind side.
- Parameters
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| dplus | Gradient approximated using RHS neighbors. |
| dminus | Gradient approximated using LHS neighbors. |
| sign | Sign of current component of the wave front velocity. |
- Returns
- Scalar upwind gradient approximation in the dimension given.
Definition at line 40 of file Upwind_gradient.hpp.
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