Related papers: Flux Globalization Based Well-Balanced Path-Conser…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
This work aims to extend the well-known high-order WENO finite-difference methods for systems of conservation laws to nonconservative hyperbolic systems. The main difficulty of these systems both from the theoretical and the numerical…
Models for shallow water flow often assume that the lateral velocity is constant over the water height. The recently derived shallow water moment equations are an extension of these standard shallow water equations. The extended models…
Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models. However, existing approaches often necessitate…
Simulations of single- and multi-species compressible flows with shock waves and discontinuities are conducted using a weighted compact nonlinear scheme (WCNS) with a newly developed sixth order localized dissipative interpolation. In…
We present a proposal for calculating the running of the coupling constant of the $\mathrm{SU}(3)$ pure-gauge theory, which combines the Twisted Gradient Flow (TGF) renormalization scheme with Parallel Tempering on Boundary Conditions…
A new Real Fluid Quasi-Conservative (RFQC) finite volume method is developed to address the numerical simulation of real fluids involving shock waves in transcritical and phase-change flows. To eliminate the spurious pressure oscillations…
This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…
In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider the Froude number ranging from O(1)…
We present a novel positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address hyperbolic conservation laws. We focus on the compressible Euler equations with strong…
This paper proposes and validates two new particle regularization techniques for the Smoothed Particle Hydrodynamics (SPH) numerical method to improve its stability and accuracy for free surface flow simulations. We introduce a general form…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
We consider the one-dimensional shallow water equations (SW) in a finite channel with variable bottom topography. We pose several initial-boundary-value problems for the SW system, including problems with transparent (characteristic)…
The active flux (AF) method is a compact high-order finite volume method that simultaneously evolves cell averages and point values at cell interfaces. Within the method of lines framework, the existing Jacobian splitting-based point value…
In this work, we present a high-order finite volume framework for the numerical simulation of shallow water flows. The method is designed to accurately capture complex dynamics inherent in shallow water systems, particularly suited for…
We derive and analyze well-posed, energy- and entropy-stable boundary conditions (BCs) for the two-dimensional linear and nonlinear rotating shallow water equations (RSWE) in vector invariant form. The focus of the study is on subcritical…
In this work, the exact reproduction of a moving-water steady flow via the numerical solution of the one-dimensional shallow water equations is studied. A new scheme based on a modified version of the HLLEM approximate Riemann solver…
We propose a new unstructured numerical subgrid method for solving the shallow water equations using a finite volume method with enhanced bathymetry resolution. The method employs an unstructured triangular mesh with support for…
A novel central weighted essentially non-oscillatory (central WENO; CWENO)-type scheme for the construction of high-resolution approximations to discontinuous solutions to hyperbolic systems of conservation laws is presented. This procedure…
We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial…