Operator splitting techniques in multidimensional systems

The first term on the right-hand side takes care of the transport processes, and the second term is the chemical source term. The operator-splitting approach treats these two terms separately and implicitly, and then combines the results explicitly to give, for the time interval n St n -j- )dt 

The approach has the advantage that the separate solutions are simpler than for the coupled system. The final step requires solution as for a homogeneous system, with the chemical source terms being solved by a standard implicit package such as Gear s method. 

The operator-splitting approach is likely to be most useful in the treatment of systems having more than one spatial dimension, for example, two-dimensional, time-dependent, boundary layer flow, where the governing equations are of the form 

The alternating direction methods, reviewed by Douglas and Gunn (1964), solve this by an operator-splitting technique as follows 

Chemical quasi-steady-state and partial equilibrium assumptions in reactive flow modeling 

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