Stability of the numerical solution of unsteady heat conduction: A mechanical approach

This work proposes a mechanical analog of the unsteady energy conservation equation for analysis of the stability of its numerical solution. The space discretized energy conservation equation is the analog of the linear momentum equation, from which no relevant information can be extracted concerning the stability of its numerical solution. The corresponding angular momentum equation can be obtained from the space discretized energy conservation equation, from which relevant information can be extracted concerning stability of the numerical solution. In that equation, the angular perturbation is the analog of the temperature perturbation. This approach/analogy and results help for a better understanding of the stability/instability of the numerical solution of unsteady diffusion problems. © 2020, © 2020 Taylor & Francis Group, LLC.