Related papers: A central-upwind scheme for open water flow in a w…
We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These…
In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special…
This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the…
Minimizing computational cost is one of the major challenges in the modelling and numerical analysis of hydrodynamics, and one of the ways to achieve this is by the use of quadtree grids. In this paper, we present an adaptive scheme on…
There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in…
Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated…
We develop a well-balanced central-upwind scheme for rotating shallow water model with horizontal temperature and/or density gradients---the thermal rotating shallow water (TRSW). The scheme is designed using the flux globalization…
In this paper, we construct a robust adaptive central-upwind scheme on unstructured triangular grids for two-dimensional shallow water equations with variable density. The method is well-balanced, positivity-preserving, and oscillation-free…
We propose a one-dimensional Saint-Venant (open channel) model overland flows including a water input--output source term modelling recharge via rainfall and infiltration (or exfiltration). We derive the model via asymptotic reduction from…
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…
Finite volume schemes for hyperbolic balance laws require a piecewise polynomial reconstruction of the cell averaged values, and a reconstruction is termed `well-balanced' if it is able to simulate steady states at higher order than time…
In this paper, we propose a novel approach for coupling 2D/1D shallow water flow models. Efficiently coupling these models is vital for simulating the flow and flooding of open channels. Currently, existing methods couple the models either…
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…
One dimensional (1D) simulations of the flow and flooding of open channels are known to be inaccurate as the flow is multi-dimensional in nature, especially at the flooded regions. However, multi-dimensional simulations, even in two…
This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm…
Simulating the flow of two fluid phases in porous media is a challenging task, especially when fractures are included in the simulation. Fractures may have highly heterogeneous properties compared to the surrounding rock matrix,…
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…
The upwind conservation element and solution element (CESE) scheme is an alternative discontinuity-capturing numerical approach to solving hyperbolic conservation laws. To evaluate the numerical properties of this spatiotemporal coupled…
Finite-volume numerical method for study shallow water flows over an arbitrary bed profile in the presence of external force is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with…
Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…