CompMath Seminar - Rick Verbiest, University of Groningen

Title: Towards spatially adaptive simulation of partial differential equations using moment models

Abstract:

The method of moments is a model reduction technique that is used to reduce the dimensionality of high-dimensional partial differential equations. This approach yields a lower-dimensional model, incorporating additional variables that encode information from the reduced dimensions through derived equations. This presentation focuses on the application of the method of moments to shallow free surface flows, characterized by a vertical length scale that is much smaller than the horizontal length scales. Additionally, the assumption of a 2D flow with radial symmetry enables the derivation and analysis of a pseudo two-dimensional model. Numerical results for both discontinuous and continuous initial conditions are presented. One of the major advantages of this model is its flexibility, as the number of moments can be adjusted based on the desired accuracy and the complexity of the underlying physics. In certain scenarios, the physical domain may exhibit regions with complex physics requiring a high-order model, alongside areas where the flow approaches equilibrium, making a low-order model sufficient. The presentation delves into the extension of moment models to spatially adaptive models, addressing the adaptability of the approach to varying complexities within different regions of the physical domain.