Mathematical problems | Computational fluid dynamics
Finite volume method for three-dimensional diffusion problem
Finite volume method (FVM) is a numerical method. FVM in computational fluid dynamics is used to solve the partial differential equation which arises from the physical conservation law by using discretisation. Convection is always followed by diffusion and hence where convection is considered we have to consider combine effect of convection and diffusion. But in places where fluid flow plays a non-considerable role we can neglect the convective effect of the flow. In this case we have to consider more simplistic case of only diffusion. The general equation for steady convection-diffusion can be easily derived from the for property by deleting transient. General transport equation is defined as: …………………………………………….1 Where, is a conservative form of all fluid flow, is density, is a net rate of flow of out of fluid element represents convective term, is a transient term, is a rate of change of due to diffusion, is a rate of increase of due to source. Due to steady state condition transient term becomes zero and due to absence of convection convective term becomes zero, therefore steady state three- dimensional convection and diffusion equation becomes: ………………………………………………………….2 Therefore, …………………………………………………………………….3 Flow should also satisfy continuity equation therefore, ………………………………………………………………………………………………………4 (Wikipedia).
