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Calculate wave speed and amplitude when solving PDE numerically
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I'm an amateur in math. I have a system of nine PDE. The system is huge and I solve it numerically by an explicit finite difference scheme. The stencil I use:
One of PDE is a reaction-diffusion that creates a wave. It has a form:
beginalign*
fracpartialpartial tT(x,y,t)=DDelta T(x,y,t) + R(T(x,y,t)) - F(T(x,y,t))
endalign*
$T(x,y,t)$ is the target function. $x,y$ are $2D$ space coordinates. $t$ is time. $R, F$ are reactions that depend on other PDE in the system.
Can I calculate how the wave of $T(x,y,t)$ is spreading? Its velocity and amplitude? I would be very grateful for a link to simple and clear materials about it.
Below is an example of waves spreading:
pde numerical-methods
asked Jul 30 at 18:51
vogdb
1064
add a comment |Â
up vote
1
down vote
favorite
I'm an amateur in math. I have a system of nine PDE. The system is huge and I solve it numerically by an explicit finite difference scheme. The stencil I use:
One of PDE is a reaction-diffusion that creates a wave. It has a form:
beginalign*
fracpartialpartial tT(x,y,t)=DDelta T(x,y,t) + R(T(x,y,t)) - F(T(x,y,t))
endalign*
$T(x,y,t)$ is the target function. $x,y$ are $2D$ space coordinates. $t$ is time. $R, F$ are reactions that depend on other PDE in the system.
Can I calculate how the wave of $T(x,y,t)$ is spreading? Its velocity and amplitude? I would be very grateful for a link to simple and clear materials about it.
Below is an example of waves spreading:
pde numerical-methods
asked Jul 30 at 18:51
vogdb
1064
Are you working with plane waves? And what kind of velocity would you like to have? For example, there are the phase velocity: en.wikipedia.org/wiki/Phase_velocity and the group velocity: en.wikipedia.org/wiki/Group_velocity
– Botond
Jul 30 at 19:02
@Botond Thank you for good questions. I work with 2d case. The wave is like a circle on the water surface. I've adjusted my post with a gif of it. Either of velocities will do fine for me. The one that is simpler to acquire is better.
– vogdb
Jul 30 at 19:44
Is linearization an option?
– Botond
Jul 30 at 20:01
I didn't understand about linearization. Linearization of what? Currently I'm solving numerically, so all functions calculations are linearised already. No?
– vogdb
Jul 31 at 7:11
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I'm an amateur in math. I have a system of nine PDE. The system is huge and I solve it numerically by an explicit finite difference scheme. The stencil I use:
One of PDE is a reaction-diffusion that creates a wave. It has a form:
beginalign*
fracpartialpartial tT(x,y,t)=DDelta T(x,y,t) + R(T(x,y,t)) - F(T(x,y,t))
endalign*
$T(x,y,t)$ is the target function. $x,y$ are $2D$ space coordinates. $t$ is time. $R, F$ are reactions that depend on other PDE in the system.
Can I calculate how the wave of $T(x,y,t)$ is spreading? Its velocity and amplitude? I would be very grateful for a link to simple and clear materials about it.
Below is an example of waves spreading:
pde numerical-methods
asked Jul 30 at 18:51
vogdb
1064
I'm an amateur in math. I have a system of nine PDE. The system is huge and I solve it numerically by an explicit finite difference scheme. The stencil I use:
One of PDE is a reaction-diffusion that creates a wave. It has a form:
beginalign*
fracpartialpartial tT(x,y,t)=DDelta T(x,y,t) + R(T(x,y,t)) - F(T(x,y,t))
endalign*
$T(x,y,t)$ is the target function. $x,y$ are $2D$ space coordinates. $t$ is time. $R, F$ are reactions that depend on other PDE in the system.
Can I calculate how the wave of $T(x,y,t)$ is spreading? Its velocity and amplitude? I would be very grateful for a link to simple and clear materials about it.
Below is an example of waves spreading:
pde numerical-methods
asked Jul 30 at 18:51
vogdb
1064
edited Jul 30 at 19:43
asked Jul 30 at 18:51
vogdb
1064
asked Jul 30 at 18:51
vogdb
1064
asked Jul 30 at 18:51
vogdb
1064
1064
Are you working with plane waves? And what kind of velocity would you like to have? For example, there are the phase velocity: en.wikipedia.org/wiki/Phase_velocity and the group velocity: en.wikipedia.org/wiki/Group_velocity
– Botond
Jul 30 at 19:02
@Botond Thank you for good questions. I work with 2d case. The wave is like a circle on the water surface. I've adjusted my post with a gif of it. Either of velocities will do fine for me. The one that is simpler to acquire is better.
– vogdb
Jul 30 at 19:44
Is linearization an option?
– Botond
Jul 30 at 20:01
I didn't understand about linearization. Linearization of what? Currently I'm solving numerically, so all functions calculations are linearised already. No?
– vogdb
Jul 31 at 7:11
add a comment |Â
Are you working with plane waves? And what kind of velocity would you like to have? For example, there are the phase velocity: en.wikipedia.org/wiki/Phase_velocity and the group velocity: en.wikipedia.org/wiki/Group_velocity
– Botond
Jul 30 at 19:02
@Botond Thank you for good questions. I work with 2d case. The wave is like a circle on the water surface. I've adjusted my post with a gif of it. Either of velocities will do fine for me. The one that is simpler to acquire is better.
– vogdb
Jul 30 at 19:44
Is linearization an option?
– Botond
Jul 30 at 20:01
I didn't understand about linearization. Linearization of what? Currently I'm solving numerically, so all functions calculations are linearised already. No?
– vogdb
Jul 31 at 7:11
Are you working with plane waves? And what kind of velocity would you like to have? For example, there are the phase velocity: en.wikipedia.org/wiki/Phase_velocity and the group velocity: en.wikipedia.org/wiki/Group_velocity
– Botond
Jul 30 at 19:02
Are you working with plane waves? And what kind of velocity would you like to have? For example, there are the phase velocity: en.wikipedia.org/wiki/Phase_velocity and the group velocity: en.wikipedia.org/wiki/Group_velocity
– Botond
Jul 30 at 19:02
@Botond Thank you for good questions. I work with 2d case. The wave is like a circle on the water surface. I've adjusted my post with a gif of it. Either of velocities will do fine for me. The one that is simpler to acquire is better.
– vogdb
Jul 30 at 19:44
@Botond Thank you for good questions. I work with 2d case. The wave is like a circle on the water surface. I've adjusted my post with a gif of it. Either of velocities will do fine for me. The one that is simpler to acquire is better.
– vogdb
Jul 30 at 19:44
Is linearization an option?
– Botond
Jul 30 at 20:01
Is linearization an option?
– Botond
Jul 30 at 20:01
I didn't understand about linearization. Linearization of what? Currently I'm solving numerically, so all functions calculations are linearised already. No?
– vogdb
Jul 31 at 7:11
I didn't understand about linearization. Linearization of what? Currently I'm solving numerically, so all functions calculations are linearised already. No?
– vogdb
Jul 31 at 7:11
add a comment |Â
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Are you working with plane waves? And what kind of velocity would you like to have? For example, there are the phase velocity: en.wikipedia.org/wiki/Phase_velocity and the group velocity: en.wikipedia.org/wiki/Group_velocity
– Botond
Jul 30 at 19:02
@Botond Thank you for good questions. I work with 2d case. The wave is like a circle on the water surface. I've adjusted my post with a gif of it. Either of velocities will do fine for me. The one that is simpler to acquire is better.
– vogdb
Jul 30 at 19:44
Is linearization an option?
– Botond
Jul 30 at 20:01
I didn't understand about linearization. Linearization of what? Currently I'm solving numerically, so all functions calculations are linearised already. No?
– vogdb
Jul 31 at 7:11