A two dimensional time dependent heat transport equation at the microscale is derived. A second order nite diierence scheme in both time and space is introduced and the unconditional stability of the nite diierence scheme is proved. A computational procedure is designed to solve the discretized linear system at each time step by using a preconditioned… (More)
We derive truncation error representation for the sixth order combined compact diierence (CCD) scheme for discretizing a one dimensional partial diierential equation. We also show that, for a model one dimensional convection diiusion equation, the CCD scheme produces numerical oscillatory solution, when the cell Reynolds number condition is violated.… (More)
We investigate the use of a fourth order compact nite diierence scheme for solving an one dimensional heat transport equation at the microscale. The fourth order compact scheme is used with a Crank-Nicholson type integrator by introducing an intermediate function for the heat transport equation. The new scheme is proved to be unconditionally stable with… (More)
Numerical computation techniques are proposed to solve a three dimensional time dependent microscale heat transport equation. A second order nite diierence scheme in both time and space is introduced and the unconditional stability of the nite difference scheme is proved. A computational procedure is designed to solve the resulting sparse linear system at… (More)
We develop a new two level finite difference scheme for the 1D PennesÕ bioheat equation. We further prove that the scheme is stable and convergent unconditionally. Numerical experiments for a skin-heating model are conducted.