illustrate the relative differences in computational efficiency

and numerical solution results.

Sparse Matrix Vectorized Gear (SMVGEAR) solver

Numerical solvers based on the algorithm developed by

Gear [84] have traditionally been used to obtain accurate

solutions to stiff ODE problems. The technique is an

implicit method that incorporates an automatic time step size

and error control and does not amplify errors from one step

to another. SMVGEAR is a version of the Gear algorithm

developed by Jacobson and Turco [85] to increase

computational efficiency. SMVGEAR is most efficient

when run on vector computers, but it is still faster than many

other Gear codes on non-vector platforms because of the

introduction of special sparse-matrix techniques. The

SMVGEAR algorithm implemented in the CCTM is

essentially the same as that developed by Jacobson and

Turco [85], although fairly extensive changes were made to

the original computer code to link the algorithm to the

generalized chemical mechanism processor used in the

CMAQ system and to make it conform to CMAQ coding

conventions. As with most solvers, the accuracy of the

numerical solutions and the computational efficiency of

SMVGEAR are affected by error tolerances that control

solution accuracy. The SMVGEAR uses a relative tolerance

to control the number of accurate digits and an absolute

error tolerance to control noise level. In the CCTM

implementation, a set of user-controllable tolerances are

applied to all species, and default relative and absolute

tolerances have been set to 10-3 and 10-9 ppm, respectively.

Quasi Steady-State Approximation (QSSA) solver

The QSSA solver is a low-order, explicit solver that exhibits

good stability for stiff systems. Although less accurate than

the Gear solver, many variants have been developed and

used in 3-dimensional AQMs (e.g., [86,6,10,87]). The

QSSA solver used in the CCTM is based on the algorithm in

the Regional Oxidant Model [6,88]. The CMAQ QSSA

solver is completely generalized and has been linked to the

CMAQ generalized chemical mechanism processor. Thus,

no a priori assumptions about reaction time scales are made,

nor is any mechanism-specific species lumping performed or

species steady-state relations assumed. As a consequence,

other non-generalized QSSA methods that employ lumping

techniques to ensure mass conservation may be somewhat

faster and more accurate. Nevertheless, its generality

facilitates the inclusion of multiple chemical mechanisms in

the CMAQ modeling system. The accuracy of the solver

can be controlled by, for example, the upper time step limit

(τ ulim ). After a series of tests, we currently recommend

τ ulim =1 minute. Note that τ ulim = 5 minutes was previously

used as the default.

 

 

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