High order structure-preserving methods for the water wave equations
Abstract
Statement of Work:The PI will develop a set of computational tools for solving the Shallow Water Equations in two and three dimensions.Objective:The objective of this proposed project is to establish a comprehensive study of novel high order structure-preserving methods for the water wave equations arising in various naval-relevant applications.Approach:The PI proposes to study the structure-preserving numerical methods for the water wave equations in the following directions: 1) Energy conserving methods for wave equations: The PI proposes to develop energy-conserving methods for the linear acoustic and nonlinear dispersive water wave equations. Detailed numerical analysis of these methods, including stability and error estimate, will be carried out. 2) Well-balanced methods for the shallow water equations: The PI will develop accurate well-balanced numerical methods which preserve the steady-state solutions exactly at the discrete level, for the shallow water equations and other dispersive water wave equations. Theoreticalnumerical analysis on the asymptotic stability of the proposed well-balanced method will be carried out to ensure the good long-time behavior. 3) Positivity-preserving methods for the water wave equations: The PI will explore simple, mass-conserving, positivity-preserving methods for the shallow water equations, and couple them with the proposedwell-balanced techniques.Overall Merit and ONR Mission/Relevance:The PI will use state-of-the-art physics-based models to analyze an important set of nonlinear partial differentialequations. This effort, if successful, will enhance the Navy and the DoD s capabilities in addressing numerical methods for oceanic and atmospheric processes.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141612714
Entities
People
- Yulong Xing
Organizations
- Office of Naval Research
- United States Navy
- University of California Regents