6 papers · 1 filter
Structure-Preserving Discontinuous Galerkin Methods for Stochastic Shallow Water Equations
Yekaterina Epshteyn, Akil Narayan, Yinqian Yu
Shallow water equations (SWE) are fundamental models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. In many practical appl…
Energy Stable and Structure-Preserving Algorithms for the Stochastic Galerkin System of 2D Shallow Water Equations
Yekaterina Epshteyn, Akil Narayan, Yinqian Yu
Shallow water equations (SWE) are fundamental nonlinear hyperbolic PDE-based models in fluid dynamics that are essential for studying a wide range of geophysical and engineering ph…
Energy Stable and Structure-Preserving Schemes for the Stochastic Galerkin Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonline…
Adaptive Central-Upwind Scheme on Triangular Grids for the Saint-Venant System
Yekaterina Epshteyn, Thuong Nguyen
In this work, we develop a robust adaptive well-balanced and positivity-preserving central-upwind scheme on unstructured triangular grids for shallow water equations. The numerical…
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
A stochastic Galerkin formulation for a stochastic system of balanced or conservation laws may fail to preserve hyperbolicity of the original system. In this work, we develop hyper…
Difference Potentials Method for Models with Dynamic Boundary Conditions and Bulk-Surface Problems
Yekaterina Epshteyn, Qing Xia
In this work, we consider parabolic models with dynamic boundary conditions and parabolic bulk-surface problems in 3D. Such partial differential equations based models describe phe…