Finite Differences: how to implement Dirichlet boundary conditions when ghost points are needed?
I have trouble understanding how you should handle Dirichlet boundary conditions for a finite difference problem when your discretization stencil goes outside your domain. For example for a 1D heat problem heat equation , you can impose a certain temperature on the boundary, for example u_1=0. But if the discretization scheme uses 5 points and is a central difference scheme, the heat equation for the second point in the domain would need a point outside of the domain. So my initial thought was to add a ghost cell, but I have no idea how to add an additional equation for this ghost point to make the problem solvable. Or is this maybe not right way to solve this?
pde finite-differences
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kak
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I have trouble understanding how you should handle Dirichlet boundary conditions for a finite difference problem when your discretization stencil goes outside your domain. For example for a 1D heat problem heat equation , you can impose a certain temperature on the boundary, for example u_1=0. But if the discretization scheme uses 5 points and is a central difference scheme, the heat equation for the second point in the domain would need a point outside of the domain. So my initial thought was to add a ghost cell, but I have no idea how to add an additional equation for this ghost point to make the problem solvable. Or is this maybe not right way to solve this?
pde finite-differences
asked 2 days ago
kak
11
New contributor
kak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I have trouble understanding how you should handle Dirichlet boundary conditions for a finite difference problem when your discretization stencil goes outside your domain. For example for a 1D heat problem heat equation , you can impose a certain temperature on the boundary, for example u_1=0. But if the discretization scheme uses 5 points and is a central difference scheme, the heat equation for the second point in the domain would need a point outside of the domain. So my initial thought was to add a ghost cell, but I have no idea how to add an additional equation for this ghost point to make the problem solvable. Or is this maybe not right way to solve this?
pde finite-differences
asked 2 days ago
kak
11
New contributor
kak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have trouble understanding how you should handle Dirichlet boundary conditions for a finite difference problem when your discretization stencil goes outside your domain. For example for a 1D heat problem heat equation , you can impose a certain temperature on the boundary, for example u_1=0. But if the discretization scheme uses 5 points and is a central difference scheme, the heat equation for the second point in the domain would need a point outside of the domain. So my initial thought was to add a ghost cell, but I have no idea how to add an additional equation for this ghost point to make the problem solvable. Or is this maybe not right way to solve this?
pde finite-differences
pde finite-differences
asked 2 days ago
kak
11
New contributor
kak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
kak
11
New contributor
kak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 17 hours ago
asked 2 days ago
kak
11
New contributor
kak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
kak
11
asked 2 days ago
kak
11
11
New contributor
kak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
kak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
kak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
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