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Our goal was to develop a robust algorithm for numerical simulation of one-dimensional shallow-water flow in a complex multiply-connected channel network with arbitrary geometry and variable topography. We apply a central-upwind scheme with…

Numerical Analysis · Mathematics 2020-04-07 Sergii Kivva , Mark Zheleznyak , Alexander Pilipenko , Vasyl Yoschenko

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…

Fluid Dynamics · Physics 2019-12-11 Valerio Caleffi , Alessandro Valiani

The fluid flow transport and hydrodynamic problems often take the form of hyperbolic systems of conservation laws. In this work we will present a new scheme of finite volume methods for solving these evolution equations. It is a family of…

Numerical Analysis · Mathematics 2021-05-25 Moussa Ziggaf , Mohamed Boubekeur , Imad kissami , Fayssal Benkhaldoun , Imad El Mahi

We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary…

Fluid Dynamics · Physics 2015-04-16 Suchuan Dong , Jie Shen

A reliable and fast numerical scheme is crucial for the 1D simulation of blood flow in compliant vessels. In this paper, a 1D blood flow model is incorporated with a Kelvin-Voigt viscoelastic arterial wall. This leads to a nonlinear…

Medical Physics · Physics 2014-09-17 Xiaofei Wang , Jose-Maria Fullana , Pierre-Yves Lagrée

The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes with variable sections. Firstly, we detail the derivation of the mathematical model in curvilinear…

Analysis of PDEs · Mathematics 2008-12-02 Christian Bourdarias , Mehmet Ersoy , Stéphane Gerbi

In this paper we propose an efficient second order well balanced finite volume method for modeling complex free surface flows at the aid of a simple diffuse interface method. The employed physical model is a two-phase model derived from the…

Numerical Analysis · Mathematics 2018-08-16 Elena Gaburro , Manuel J. Castro , Michael Dumbser

After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations…

Fluid Dynamics · Physics 2020-02-20 Denys Dutykh , Didier Clamond , Paul Milewski , Dimitrios Mitsotakis

A numerical scheme of relaxation type is proposed to approximate hyperbolic conservation laws in canal networks. Physical conditions at the junction are given and a novel strategy based on [Briani, Natalini, Ribot, 2025] is introduced to…

Numerical Analysis · Mathematics 2025-12-03 Tommaso Tenna

One-dimensional (1D) blood flow simulations are extensively used in cardiovascular research due to their computational efficiency and effectiveness in analyzing pulse wave dynamics. Despite their versatility and simplicity, there is a lack…

Quantitative Methods · Quantitative Biology 2025-08-27 Daehyun Kim , Jeffrey Tithof

We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by…

Computational Physics · Physics 2016-04-29 Alexandros Syrakos , Georgios C. Georgiou , Andreas N. Alexandrou

We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…

Numerical Analysis · Mathematics 2020-08-05 Jonas P. Berberich , Praveen Chandrashekar , Christian Klingenberg

Since the celebrated theorem of Lax and Wendroff, we know a necessary condition that any numerical scheme for hyperbolic problem should satisfy: it should be written in flux form. A variant can also be formulated for the entropy. Even…

Numerical Analysis · Mathematics 2023-04-19 Remi Abgrall

Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system,…

Numerical Analysis · Mathematics 2020-11-05 José A. Carrillo , Serafim Kalliadasis , Sergio P. Perez , Chi-Wang Shu

We study a finite volume scheme for the approximation of the solution to convection diffusion equations with nonlinear convection and Robin boundary conditions. The scheme builds on the interpretation of such a continuous equation as the…

Numerical Analysis · Mathematics 2022-09-13 Clément Cancès , Juliette Venel

Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…

Fluid Dynamics · Physics 2026-05-13 Ye Wang , Armin Wehrfritz , Evatt R. Hawkes

The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-volume numerical methods for 1D systems of balance laws. The strategy introduced by two of the authors in a previous paper for explicit schemes…

Numerical Analysis · Mathematics 2022-08-31 Irene Gómez-Bueno , Sebastiano Boscarino , Manuel Jesús Castro , Carlos Parés , Giovanni Russo

We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments…

Numerical Analysis · Mathematics 2015-05-13 Matania Ben-Artzi , Joseph Falcovitz , Philippe G. LeFloch

This study investigates the hemodynamic behavior of blood flow in the aortic arch across anemic, diabetic, and healthy conditions using computational fluid dynamics (CFD) simulations with a non-Newtonian Carreau viscosity model. Velocity…

Fluid Dynamics · Physics 2025-06-23 Farzana Akter Tina , Hashnayne Ahmed , Hena Rani Biswas

The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes. Firstly, we detail the mathematical model written as a conservative hyperbolic partial differentiel…

Analysis of PDEs · Mathematics 2010-06-02 Christian Bourdarias , Stéphane Gerbi