Jennifer J. Zhao

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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)
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