Class of conservative under stabilization numerical simulation algorithms for transfer processes (Q2739965)

This paper deals with two-steps symmetrized algorithms for the numerical solution of the boundary value problem for the equation NEWLINE\[NEWLINE{\partial u\over \partial t}= -\sum\limits_{s=1}^{3}v_{s}{\partial u\over \partial x^{(s)}}+ \sum\limits_{s=1}^{3}\theta_{s} {\partial^2 u\over \partial {x^{(s)}}^2}+bu+f(x^{(1)},x^{(2)},x^{(3)},t)NEWLINE\]NEWLINE in the domain \(Q=\{(0\leq t\leq T)\times G\}\), \(G=\{0\leq x^{(s)} \leq 1, s=1,2,3\}\) with the initial condition \(u|_{t=0}= \phi((x^{(1)},x^{(2)},x^{(3)})\) and the boundary condition \({\partial u\over\partial n}_{S}+\beta u|_{S}=\gamma\), where \(S\) is the boundary of \(Q\). The author considers a center-by-difference approximation and approximations by an opposite flow difference of the convective terms of the equation. The unconditional stability of the algorithms is proved and the conservatism of difference algorithms under stabilization of the process is established.