NOTE: This repo was imported from here
In this repo is a very simple implementation of an application for solving the one dimensional heat conduction equation. This is the functional equivalent of a Hello World application for HPC/CSE numerical programmers.
In general, heat conduction is governed by the partial differential (PDE)...
| (1) |
where u is the temperature at spatial positions, x, and times, t,
is the thermal diffusivity
of the homogeneous material through which heat is flowing. This partial differential equation (PDE)
is known as the Diffusion Equation and also the Heat Equation.
To make the problem tractable for this lesson, we make some simplifying assumptions...
- The thermal diffusivity,
, is constant for all space and time.
- The only heat source is from the initial and/or boundary conditions.
- We will deal only with the one dimensional problem in Cartesian coordinates.
In this case, the PDE our application needs to solve simplifies to...
| (2) |
Currently, three different numerical algorithms are implemented
- Foward Time Centered Space (FTCS), an explicit method
- Crank-Nicholson, an implicit method
- Upwind-15, another explicit method with higher spatial order than FTCS.
The technical details are described more fully in this ATPESC Hands-On Lesson