A one dimensional advection-diffusion problem solved via an arbitrary precision generalized solution

CARLOS FILIPICH; MARTA ROSALES; ELBIO D. PALMA

San Pablo, Brasil

Congreso; Computational Methods in Engineering'99; 1999

An alternative approach to solve the one-dimensional advection-diffusion(transport) equation is presented. The methodology is named WEM (Whole Element Method)and starts from a systematic stating of extremizing sequences of functions belonging to an apriori complete set. The scope of WEM includes the solution of boundary value problems inone, two or three dimensional domains and also initial-boundary value problems as in thepresent case. The essential boundary conditions are imposed to the complete sequence andnot, unlike Ritz methods, to each coordinate function. Eventual non-satisfied conditions aretaken into account by Lagrange multipliers. After a suitable transformation an ad hocfunctional for the title problem is derived. Two examples of propagation and dispersion of aninitial concentration in an infinite channel are numerically solved and tested againstanalytical and numerical solutions obtained with standard techniques. Additionally, althoughincluded in the transport equation, an advection domminated flow is analyzed with certaindetail since it poses a practical problem for approximate solutions. The results show that theproposed method is very accurate even for low diffusion problems and lacks from dissipationwhen dealing with advection dominated flow problems.