How to Save Computational Time with a OneWay Coupling Approach
Phillip Oberdorfer September 6, 2017
When simulating heat transfer in fluids with forced convection, we can often neglect the influence of temperature variations on the flow field unless the requirements on accuracy are very high. Computing the flow field independently might substantially decrease the computational cost with a negligible impact on accuracy in the solution. In this blog post, we demonstrate the advantages of using a oneway coupling in the COMSOL Multiphysics® software with a nonisothermal flow example.
The Benefits of a OneWay Coupling Approach
You can save a lot of computational time when running a simulation if the impact of temperature variations on the flow field are negligible compared to the accuracy required for the solution. In such cases, we can compute the flow field in the first study step and then use it as an input for the heat transfer problem solved in the second study step, which is an easy thing to do in COMSOL Multiphysics.
Instead of solving a twoway coupled problem (flow ↔ transport), we solve a simpler oneway coupled problem (flow → transport). The reduction in computational time and memory is even higher if the solution of the flow field can be reused several times; e.g., when a parametric study for different heat transfer conditions is carried out for the same flow field.
The oneway coupling approach can be applied for all types of fluid flow, including turbulent regimes and flow in porous media. It is also possible to apply this technique to any advected field, provided that the coupling is weak; e.g., for chemical species transport in dilute solutions.
The important criterion for the validity of the oneway coupling approach is that the influence on the flow field, assuming a constant temperature, is much smaller than the accuracy required in the computation. We have to check that the variations in density and viscosity caused by temperature changes are small enough that their impact on the flow fields falls within the accuracy limit in the analyses. It is recommended to assume the flow mean temperature as the reference temperature for density and viscosity in the oneway coupled case.
The best way to check the validity of a oneway coupled approach is to solve a test model and compare the results to a twoway coupled solution of the same problem. Pick a few sample points in the analysis where the fully coupled problem is computed and verify the simplified approach against the full solution. If these points fall within the required accuracy, we can use the simplified approach for the bulk of the computations. The samples need to be selected wisely, as the verification points must fall inside the simulation window of operation. Ideally, these points should be the extreme conditions and all other computations should fall within the extreme points.
If it turns out that the oneway coupling is not a suitable simplification for a certain simulation task, using this technique can still be helpful. The approach of solving the decoupled problem first is a good option to get good initial guesses for the fully coupled problem for steady nonisothermal flows. There are cases where the flow field does not converge unless a decent initial guess is provided, which is what we can obtain with the approach discussed here.
Modeling a CrossFlow Heat Exchanger with a OneWay Coupling
Let’s try out the oneway coupling approach using the CrossFlow Heat Exchanger tutorial model. This type of heat exchanger is found in labonachip devices in biotechnology and microreactors, such as for microsized fuel cells.
The modeled part of the microsized heat exchanger.
The modeled system consists of two sets of channels, one hot and one cold, arranged in a crossflow pattern with five channels in each set, as shown in the figure above. The model is reduced due to the symmetry of the heat exchanger.
If we check the study nodes of the model, we find two stationary study steps. In the first study step, only laminar flow (spf) is selected for solving, while in the second study step, heat transfer (ht) is selected together with the multiphysics coupling nonisothermal flow (nitf1). The flow field is solved in the first study step and the result is automatically taken in the second step because of the applied coupling provided by the Nonisothermal Flow multiphysics node. This study setup is preset; available as of COMSOL Multiphysics version 5.3; and called Stationary, OneWay Coupled, NITF for stationary simulations and Time Dependent, OneWay Coupled, NITF for transient simulations.
Comparing the Results for the OneWay and TwoWay Couplings
We can compare the results of the oneway coupled approach with a twoway coupled version by adding a new study with a stationary, fully coupled study step. After computing both studies, it turns out that the results vary only slightly. The heat transfer coefficient, probably the most interesting result of the model, becomes 1547.8 W/(m^{2}K) for the twoway coupling and 1548.1 W/(m^{2}K) for the oneway coupling. The difference of less than 0.2‰ is probably a lot smaller than the numerical error in the two computations. Further, the computation time is halved — from about 3 minutes for the twoway coupled problem to less than 1.5 minutes for the oneway coupled problem.
A comprehensive comparison of the two approaches can be found in the slideshow presentation available with the model documentation.
Temperature results of the oneway coupling (left) and twoway coupling (right) stationary solutions.
If the transient behavior of the model is of interest, other study combinations are possible. For example, we can add two timedependent study steps, where the flow is solved first, followed by a transient heat transfer study step (Time Dependent, OneWay Coupled, NITF). We can also create a study sequence with a stationary flow and a transient heat transfer study if the flow conditions are not changed with time (except temperature). The table below gives an overview of the different study combinations and their respective computation times for a simulation time of 10 seconds.
Study Type  Computation Time (Seconds) 

Oneway coupled (stationary) 
77

Twoway coupled (stationary) 
183

Oneway coupled (time dependent) 
571

Twoway coupled (time dependent) 
806

Oneway coupled stationary flow and timedependent heat transfer 
246

The computation times of different study approaches on an Intel® Core™ processor E51620 @ 3.70 GHz machine.
As expected, cases where the transient heat transfer is oneway coupled with stationary flow fields are computed in less time. The demonstration problem is obviously small with respect to the computational time, but the simplified approach discussed in this blog post becomes a more important option as a problem grows.
Further Reading
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