Discretization of the Convection-Diffusion Equation Using Discrete Exterior Calculus

On solutions of convection-diffusion equation in fluid

“…For both the fractional/normal diffusion process and the ordinary case of the normal advection-diffusion phenomenon, the particular solution was obtained from the general solution. The convective term was discretized using discrete exterior calculus by Noguez et al 18 in which the stabilization of discretization is comparable to the finite element method with linear interpolation functions, was achieved through the use of established stabilization techniques like artificial diffusion. To demonstrate numerical convergence, they undertook numerical experiments on basic stationary and transient cases involving domain discretization using coarse and fine simplicial meshes.…”

“…When 0 < θ ≤ 1 temperatures at the new time level are used on both sides of the equation, and θ = 1 2 corresponds to the implicit scheme, while θ = 1 gives fully implicit Crank-Nicolson scheme. In the explicit scheme, the source term is linearized as b = S u + S p T 0 P and substituting θ = 0 into equation (18) gives the explicit form of discretization of the unsteady conductive heat transfer equation…”

High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations

“…For different model equations, researchers will use different numerical methods. For example, a local discrete exterior calculus discretization [8] of the convection diffusion equation for compressible and incompressible flow is proposed, and the discretization needs to be stabilized by introducing artificial diffusion. For the CDR equation, the numerical methods mainly include finite element method [9][10][11][12][13][14], integration factor method [15][16][17][18], meshless method [1,19], finite difference (FD) method [20][21][22][23][24][25][26][27][28], and so on.…”