How do you communicate and visualize the results and insights of ROM for CFD nonlinear and chaotic systems?

1 Why nonlinear and chaotic systems are challenging

Nonlinear and chaotic systems are systems that exhibit complex and unpredictable behavior due to the presence of nonlinearities, feedback loops, bifurcations, and sensitive dependence on initial conditions. These systems are common in many CFD applications, such as turbulence, combustion, fluid-structure interaction, and multiphase flow. Nonlinear and chaotic systems pose some challenges for ROM, because they require more careful selection of the basis functions, parameters, and error metrics that capture the essential dynamics of the system. Moreover, they can make the ROM results difficult to communicate and visualize, because they can have multiple modes, transitions, and uncertainties that are not easily represented by conventional plots and graphs.

2 How to select the right ROM method

When selecting a ROM method for CFD nonlinear and chaotic systems, it is important to consider the type and amount of data available, the dimensionality and complexity of the system, as well as the accuracy and robustness of the model. Proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), balanced truncation (BT), and nonlinear manifold learning (NML) are all ROM methods that can be used for this purpose. Some methods require full-field snapshots of the system, while others can work with sparse or noisy data. Additionally, some methods are more suitable for low-dimensional or linear systems, while others can handle high-dimensional or nonlinear systems. Furthermore, some ROM methods can provide more accurate or robust models than others, depending on the error metrics, regularization techniques, and validation methods used. Finally, some ROM methods can quantify the uncertainty or sensitivity of the model, while others can only provide point estimates.

4 How to communicate the ROM insights

To effectively communicate and convey the insights and implications of your ROM for your CFD nonlinear and chaotic system, you need to use effective communication skills and strategies when presenting to your audience. Firstly, you should define your purpose and audience, tailoring your message and tone to suit their background and expectations. Secondly, you should use clear and concise language to avoid ambiguity or confusion, while also using appropriate terminology, definitions, and explanations. Thirdly, relevant visuals can help support your ROM insights and arguments; choose the right type of visuals with appropriate labels, captions, colors, and scales. Fourthly, a logical and persuasive structure should be used to organize your ROM insights; follow a clear sequence with transitions, signposts, and summaries. Finally, feedback and interaction can enhance communication; invite questions or comments from your audience, seek feedback from peers or mentors, and respond constructively.