SPLE - Structure-Preserving Lagrangian schemes for fluid mechanics applied to clean energy production

Abstract:

The goal of this project is to design, analyze, and implement innovative numerical methods for simulating physical processes relevant to clean energy production, including hydroelectric power generation and nuclear fusion. These complex phenomena are governed by nonlinear systems of partial differential equations, with the models considered in this study based on the compressible Navier-Stokes equations for fluid dynamics and the ideal magnetohydrodynamic (MHD) system for plasma flows.

A key challenge in numerical modeling is ensuring that the discrete schemes preserve the fundamental mathematical properties of the underlying physical models. To achieve this, the project focuses on the development of structure-preserving numerical schemes that maintain critical invariants and physical constraints at the discrete level. By constructing consistent and physically reliable discrete operators, these methods will enable the accurate and robust simulation of complex fluid and plasma dynamics, ultimately advancing computational tools for clean energy applications that benefit society.