Mixing
Application of Gauss-Green Law to Partial Derivativeterm in Differential Equation
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Simple question, just confused about something. I am simply trying to turn a PDE in to an integral equation for use in a finite volume scheme by using Gauss-Green theorem and am confused about a term.
$c_1frac{partial T}{partial t} = frac{partial f_i}{partial x_i} + c_2frac{partial a}{partial t}|_{x,y,z} $
The $f_i$ is a flux vector. The last term ($ c_2frac{partial a}{partial t}|_{x,y,z} $) is a scalar term, the $c_2, a$ and $t$ are all scalars. I'm not sure what it should look like after I've applied Gauss-Green theorem. I think its the $|_{x,y,z}$ that is causing me great confusion.
My attempt at converting the PDE to an integral equation is
$ int_V c_1 frac{partial T}{partial t}dV = int_S (f_i dot{} n_i)dS + int_V (c_2frac{partial a}{partial t}|_{x,y,z} )dV$
It would nice if somebody could confirm this or correct me if I am wrong. Again, my confusing lies with the $ |_{x,y,z}$ thing.
pde numerical-methods
asked Jan 30 at 23:42
ajh1111ajh1111
11
$endgroup$
add a comment |
$begingroup$
Simple question, just confused about something. I am simply trying to turn a PDE in to an integral equation for use in a finite volume scheme by using Gauss-Green theorem and am confused about a term.
$c_1frac{partial T}{partial t} = frac{partial f_i}{partial x_i} + c_2frac{partial a}{partial t}|_{x,y,z} $
The $f_i$ is a flux vector. The last term ($ c_2frac{partial a}{partial t}|_{x,y,z} $) is a scalar term, the $c_2, a$ and $t$ are all scalars. I'm not sure what it should look like after I've applied Gauss-Green theorem. I think its the $|_{x,y,z}$ that is causing me great confusion.
My attempt at converting the PDE to an integral equation is
$ int_V c_1 frac{partial T}{partial t}dV = int_S (f_i dot{} n_i)dS + int_V (c_2frac{partial a}{partial t}|_{x,y,z} )dV$
It would nice if somebody could confirm this or correct me if I am wrong. Again, my confusing lies with the $ |_{x,y,z}$ thing.
pde numerical-methods
asked Jan 30 at 23:42
ajh1111ajh1111
11
$endgroup$
add a comment |
$begingroup$
Simple question, just confused about something. I am simply trying to turn a PDE in to an integral equation for use in a finite volume scheme by using Gauss-Green theorem and am confused about a term.
$c_1frac{partial T}{partial t} = frac{partial f_i}{partial x_i} + c_2frac{partial a}{partial t}|_{x,y,z} $
The $f_i$ is a flux vector. The last term ($ c_2frac{partial a}{partial t}|_{x,y,z} $) is a scalar term, the $c_2, a$ and $t$ are all scalars. I'm not sure what it should look like after I've applied Gauss-Green theorem. I think its the $|_{x,y,z}$ that is causing me great confusion.
My attempt at converting the PDE to an integral equation is
$ int_V c_1 frac{partial T}{partial t}dV = int_S (f_i dot{} n_i)dS + int_V (c_2frac{partial a}{partial t}|_{x,y,z} )dV$
It would nice if somebody could confirm this or correct me if I am wrong. Again, my confusing lies with the $ |_{x,y,z}$ thing.
pde numerical-methods
asked Jan 30 at 23:42
ajh1111ajh1111
11
$endgroup$
Simple question, just confused about something. I am simply trying to turn a PDE in to an integral equation for use in a finite volume scheme by using Gauss-Green theorem and am confused about a term.
$c_1frac{partial T}{partial t} = frac{partial f_i}{partial x_i} + c_2frac{partial a}{partial t}|_{x,y,z} $
The $f_i$ is a flux vector. The last term ($ c_2frac{partial a}{partial t}|_{x,y,z} $) is a scalar term, the $c_2, a$ and $t$ are all scalars. I'm not sure what it should look like after I've applied Gauss-Green theorem. I think its the $|_{x,y,z}$ that is causing me great confusion.
My attempt at converting the PDE to an integral equation is
$ int_V c_1 frac{partial T}{partial t}dV = int_S (f_i dot{} n_i)dS + int_V (c_2frac{partial a}{partial t}|_{x,y,z} )dV$
It would nice if somebody could confirm this or correct me if I am wrong. Again, my confusing lies with the $ |_{x,y,z}$ thing.
pde numerical-methods
pde numerical-methods
asked Jan 30 at 23:42
ajh1111ajh1111
11
asked Jan 30 at 23:42
ajh1111ajh1111
11
asked Jan 30 at 23:42
ajh1111ajh1111
11
asked Jan 30 at 23:42
ajh1111ajh1111
11
asked Jan 30 at 23:42
ajh1111ajh1111
11
11
add a comment |
add a comment |
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