Structure-preserving shallow water moment models for free surface flows
Abstract
A fundamental challenge for the US Navy is to keep the worlds waters safe and productive.Beyond the strategic allocation and safe maneuvering of naval assets, a clear challenge to this mission is the introduction of extreme weather events. Predicting the dynamicbehavior of extreme weather events is fundamentally challenging due to the extreme scales involved. Recent technological advancements have facilitated precise three-dimensional (3D) simulations that capture the complex dynamics of tornadoes. The same fundamentalphysics governs the formation of hurricanes, however the vast scales involved make direct 3D simulations impractical if not imposable. The Earth s circumference stretches approximately 24,900 miles, while the majority of atmospheric activity is confined to a layer just 10 miles thick. This discrepancy in scales renders it impossible to resolve both vertical and horizontal dimensions concurrently. Consequently, this scale separation has given rise to various modeling techniques, with the shallow water equations standing out as a principal approach. However, shallow water equations can not capture vertical information, and hence predicting the formation as well as dynamics of a hurricane is beyond what the shallow water equations were designed to accomplish. This proposal seeks togenerate a new class of generalized shallow water models capable of naturally incorporating vertical flow information. The main idea is to take moments of the vertical direction of the incompressible Navier Stokes equations as a path to deriving models that can describe vertical motion in the context of shallow water equations. Such an expansion will provide increased fidelity but may still lack some of the predictive nature of what we seek to accomplish. To that end this proposal seeks to develop blended computing models which leverage ideas from data-driven modeling to create surrogates that augment low fidelity models in a manner that allows them to capture high fidelity effects at the cost of the low fidelity models. The approach seeks to capture high fidelity predictions over a broad range of scales. Self-consistent surrogate models come in the form of reduced basis methods, reduced order models, and neural networks designed to preserve key mathematical structures. The PIs are leaders in the development and analysis of blended computing models and associated numerical algorithms. The PIs seek to leverage their expertise to develop a new set of extended shallowwater equations, and associated theory around the models, with the long-term goal of building a new class of cost-effective predictive models that can accurately capture extreme weather events.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 15, 2024
- Source ID
- N000142412242
Entities
People
- Juntao Huang
Organizations
- Office of Naval Research
- Texas Tech University System
- United States Navy