# Modified heat eq. in 3D [closed]

please how can I write gradient numerically? I have an eq. $\dfrac{\partial X}{\partial t}=\nabla^2 X + u\nabla X$ I wonder how write this in 3D. Many thanks for any idea... I can find how to solve the "pure" heat eq. but so I don't know..

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## closed as not a real question by Christian Clason, Daniel Shapero, Ben, Jan, Bill BarthJun 14 '13 at 18:45

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Hi lovis, and welcome to scicomp! I presume $X$ is a scalar quantity, right? –  Paul Feb 7 '13 at 17:32
yes, it is. Many thanks for your message. What can be done with this? –  lovis Feb 7 '13 at 17:39
Excellent. Are you using finite difference method to solve this equation as well? What order accuracy do you expect your solution to have? –  Paul Feb 7 '13 at 17:47
Do you only want to know how to discretize the gradient or how to solve the system? Can you rewrite your question to clarify? –  vanCompute Feb 7 '13 at 17:48
Your equation is called advection-diffusion equation. You may want to google for that. –  Wolfgang Bangerth Feb 8 '13 at 0:39