## How to Save Computational Time with a One-Way 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 one-way coupling in the COMSOL Multiphysics® software with a nonisothermal flow example.

### The Benefits of a One-Way 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 two-way coupled problem (flow ↔ transport), we solve a simpler one-way 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 one-way 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 one-way 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 one-way coupled case.

The best way to check the validity of a one-way coupled approach is to solve a test model and compare the results to a two-way 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 one-way 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 Cross-Flow Heat Exchanger with a One-Way Coupling

Let’s try out the one-way coupling approach using the Cross-Flow Heat Exchanger tutorial model. This type of heat exchanger is found in lab-on-a-chip 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 cross-flow 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, One-Way Coupled, NITF for stationary simulations and Time Dependent, One-Way Coupled, NITF for transient simulations.

#### Comparing the Results for the One-Way and Two-Way Couplings

We can compare the results of the one-way coupled approach with a two-way 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/(m2K) for the two-way coupling and 1548.1 W/(m2K) for the one-way 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 two-way coupled problem to less than 1.5 minutes for the one-way 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 one-way coupling (left) and two-way 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 time-dependent study steps, where the flow is solved first, followed by a transient heat transfer study step (Time Dependent, One-Way 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)
One-way coupled (stationary)
77
Two-way coupled (stationary)
183
One-way coupled (time dependent)
571
Two-way coupled (time dependent)
806
One-way coupled stationary flow and time-dependent heat transfer
246

The computation times of different study approaches on an Intel® Core™ processor E5-1620 @ 3.70 GHz machine.

As expected, cases where the transient heat transfer is one-way 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.

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1. Moustafa AlDamook January 24, 2018   6:44 pm

Hi,
We believe this is the best Blog post since we have seen and used the COMSOL Software .

Group PhD research students at university of Leeds

2. Anonymous January 25, 2018   3:17 am

Dear Moustafa,
thank you very much! I hope that the Blog post helps you to get the most of your model!

Best regards,
Phillip

3. Asal Bidarmaghz February 14, 2018   9:00 am

Dear Philip,
Many thanks for the very useful post.
I just have a question. for time dependent heat transfer-fluid flow problems, do we need to link the second study with heat transfer physic to the first (fluid flow), within the second study via values of variables solved and not solved for? or Comsol understands the physics are coupled and are common in the time (t)?

Regards,
Asal Bidarmaghz

4. Phillip Oberdorfer February 15, 2018   4:38 am

Dear Asal,

if you create a new study or a new study step for the fluid flow computation, you have to link the variables as described. COMSOL does not automatically assume that the physics are coupled because there are cases where this is not desired.

5. FERHAT MED FOUAD January 31, 2019   4:23 pm

Thanks