Interdisciplinary Applied Mathematics

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An effective hierarchical strategy for a full-system simulation employing the coupled circuit-device simulator for microfluidic applications is illustrated in Figure 1.33. This simulator supports compact models for the electronic components and available macromodels for microfluidic devices. In addition, full-physics models are available for the microfluidic components that can be utilized when detailed and accurate modeling is required. As an example, specific components such as microvalves, pumps, and flow sensors are shown in Figure 1.33. However, the list for the flow domain is much broader and could include networks of microchannels, micronozzles, as well as more complex flow systems such as a gas microturbine. The coupling of the circuit and microfluidic components is handled by imposing suitable boundary conditions on the fluid solver. This simulator allows the simulation of a complete microfluidic system including the associated control electronics. A coupled circuit/device modeling tool, CODECS (acronym for Coupled Device and Circuit Simulator), provides a truly mixed-level description of both circuits and devices. This program was developed at UC Berkeley (Mayaram and Pederson, 1987), and it employs combinations of both ODEs and PDEs with algebraic equations. CODECS incorporates SPICE3,    the    latest    version    of    SPICE    written    in C (Quarles,    1989),    for

the circuit simulation capability. The multirate dynamics introduced by combinations of devices and circuits is handled efficiently by a multilevel Newton method or a full-Newton method for transient analysis, unlike the standard Newton method employed in SPICE. CODECS is appropriate for one-dimensional and two-dimensional devices, but other developments have produced efficient algorithms for three-dimensional devices as well (Mayaram et al., 1993).

In coupled-domain problems, such as flow-structure, structure-electric, or a combination of both, there are significant disparities in temporal and spatial scales. This, in turn, implies that multiple grids and heterogeneous time-stepping algorithms may be needed for discretization, leading to very complicated and consequently computationally prohibitive simulation algorithms. The main disadvantage of a full-system simulation approach is the high computational cost involved. The principal cost comes from solving the three-dimensional time-dependent flow equations in complex geometric domains, in transition regimes, and with unfamiliar physics. It is therefore important to obtain a fundamental understanding of microflows and nanoflows first in order to construct low-dimensional models similar to what has been done in flows at large scales (see, for example, (Berkooz et al., 1993; Deane et al., 1991; Ball et al., 1991)), and second to explore new design concepts based on new physics.

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