TY - JOUR ID - 15728 TI - Discretization of the 2D Convection–Diffusion Equation Using ‎Discrete Exterior Calculus JO - Journal of Applied and Computational Mechanics JA - JACM LA - en SN - AU - Noguez, Marco A. AU - Botello, Salvador AU - Herrera, Rafael AU - Esqueda, Humberto AD - Centro de Investigación en Matemáticas A.C. CIMAT, Jalisco S/N, Col. Valenciana, Guanajuato, Gto, 36023, México Y1 - 2020 PY - 2020 VL - 6 IS - Special Issue SP - 1348 EP - 1363 KW - Discrete Exterior Calculus KW - Finite element analysis KW - Transport Equation KW - Compressible and Incompressible Flow KW - convection KW - ‎Advection KW - Diffusion DO - 10.22055/jacm.2020.34246.2370 N2 - While the Discrete Exterior Calculus (DEC) discretization of the diffusive term of the Transport Equation is well understood, the DEC discretization of the convective term, as well as its stabilization, is an ongoing area of research. In this paper, we propose a local discretization for this term based on DEC and geometric arguments, considering the particle velocity field prescribed at the vertices of the primal mesh. This formulation is similar to that of the Finite Element Method with linear interpolation functions (FEML) and can be stabilized using known stabilization techniques, such as Artificial Diffusion. Using this feature, numerical tests are carried out on simple stationary and transient problems with domains discretized with coarse and fine simplicial meshes to show numerical convergence. UR - https://jacm.scu.ac.ir/article_15728.html L1 - https://jacm.scu.ac.ir/article_15728_f1f7c8d3684192ad6f0a5f668a5a82ba.pdf ER -