# Solving the diffusion/heat equation for a randomly distributed set of points in 3D

In this problem I am trying to solve, I have a messy set of points distributed in 3D space, each with a defined temperature. If I would want to calculate the heat transfer scenario in this system, how would you recommend me an approach (numerically and with each computational tool)? I thought about triangulating the points and using a unstructured grid Finite Volume Method. Considering the maths around this is a bit harder than that of a structured grid, I assumed the possibility of interpolating the unstructured grid into a structured grid, solving the discretized diffusion model and then interpolating back to the unstructured grid.

• What do you mean by "calculate the heat transfer scenario"? Apr 24, 2018 at 16:03
• Solving the transient heat equation Apr 24, 2018 at 17:18
• What I understand from your first sentence is that you already knew the temperature at the points. Apr 24, 2018 at 17:22
• Yes, but I want to calculate the temperature field (at each point) in the next instant in time considering thermal diffusion. Apr 24, 2018 at 17:26
• But we don't know how heat is transferred. Are the points connected by little rods that transport heat? Are the points part of a homogenous medium? An imhomogenous medium? If it is part of a homogenous medium, what do you know about the initial temperature between points? Without saying what you want to do, i.e., what the exact model is, there is no correct answer to your question. Apr 25, 2018 at 4:32