Operator splitting? What is it in the context of transport modeling?

In summary, using dimensionless groups is a powerful tool for analyzing physical and chemical problems.
  • #1
bumblebee77
56
2
Hello all:

I'm a thermodynamicist wanting to get into transport modeling. In my reading, I have come across "operator splitting." I'm confused about exactly what this means in the context of transport modeling.

This is probably a silly question, but does it refer to an advective term relative to a diffusive term in a transport equation? Or does it refer to doing a thermodynamics (or equilibration/compositional) step and THEN a fluid flow step?

I have set up my own little example code to model chemical reactions during flow. I first carry out a thermodynamics step to get compositional information and then I perform a flow step. Is this operator splitting??

Thanks in advance for your patience with a rookie!
 
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  • #3
bumblebee77 said:
Hello all:

I'm a thermodynamicist wanting to get into transport modeling. In my reading, I have come across "operator splitting." I'm confused about exactly what this means in the context of transport modeling.

This is probably a silly question, but does it refer to an advective term relative to a diffusive term in a transport equation? Or does it refer to doing a thermodynamics (or equilibration/compositional) step and THEN a fluid flow step?

I have set up my own little example code to model chemical reactions during flow. I first carry out a thermodynamics step to get compositional information and then I perform a flow step. Is this operator splitting??

Thanks in advance for your patience with a rookie!
Use of dimensionless groups is a very powerful tool for analyzing physical and chemical problems. Over the years, I have come to recognize that all physical systems are more fundamentally described in terms of their dimensionless groups than in terms of the individual parameters associated with the system. So for example, even though the total number of physical parameters involved may be 8, the number of dimensionless groups involved may only be 4 or 5. This allows the results to calculations to be presented once and for all in terms of the limited number of dimensionless groups rather than in terms of varying the individual parameters. This makes the results much easier to understand and more concise. And, if a system behavior is being examined experimentally, it reduces the number of experiments needed to quantify the range of behavior. Finally, straightforward methods have been developed for reducing the differential equations or algebraic equations for a system to dimensionless form so that the behavior can be directly determined in terms of the key dimensionless groups.
 
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1. What is operator splitting in the context of transport modeling?

Operator splitting is a numerical method used in transport modeling to solve partial differential equations (PDEs) that describe the transport of a quantity, such as heat or mass. It involves breaking down the PDE into smaller, simpler equations that can be solved separately, and then combining the solutions to obtain an overall solution.

2. How does operator splitting work?

Operator splitting works by splitting the original PDE into smaller, simpler equations, typically using the method of characteristics. These smaller equations can be solved separately using numerical techniques, such as finite difference or finite element methods. The solutions from each equation are then combined to obtain an overall solution for the original PDE.

3. What are the advantages of using operator splitting?

One advantage of using operator splitting is that it allows for the use of different numerical methods for each equation, which can be beneficial for solving complex or nonlinear PDEs. It also reduces the computational cost compared to solving the original PDE directly, making it a more efficient method for transport modeling.

4. What are the limitations of operator splitting?

One limitation of operator splitting is that it may introduce errors in the overall solution, especially if the smaller equations are not solved accurately or if there are strong interactions between the equations. It also requires careful consideration of the splitting scheme and the order in which the equations are solved to ensure stability and accuracy.

5. In what applications is operator splitting commonly used?

Operator splitting is commonly used in transport modeling applications, such as in fluid dynamics, heat transfer, and chemical reactions. It is also used in other fields, such as image processing and financial modeling, where PDEs are used to describe dynamic systems.

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