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This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…

Fluid Dynamics · Physics 2015-07-21 Carmine Di Nucci

Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…

chao-dyn · Physics 2016-08-31 A. J. Roberts

This study introduces a hybrid fluid simulation approach that integrates generative diffusion models with physics-based simulations, aiming at reducing the computational costs of flow simulations while still honoring all the physical…

We derive a homogenized macroscopic model for fluid flows over ordered homogeneous porous surfaces. The unconfined free-flow is described by the Navier-Stokes equation, and the Darcy equation governs the seepage flow within the porous…

Fluid Dynamics · Physics 2021-01-20 Y. Sudhakar , Ugis Lacis , Simon Pasche , Shervin Bagheri

We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…

Fluid Dynamics · Physics 2025-10-01 Nidia Reyes-Gil , Greg Thomsen , Kristopher Rowe , Peter Diamessis

It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…

Fluid Dynamics · Physics 2014-08-04 Maxim Zaytsev , Vyacheslav Akkerman

A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…

Fluid Dynamics · Physics 2014-08-11 Jun-De Li

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software…

Computational Engineering, Finance, and Science · Computer Science 2011-07-21 Mikael Mortensen , Hans Petter Langtangen , Garth N. Wells

Many fundamental problems in fluid dynamics are related to the effects of solid boundaries. In general, they install sharp gradients and contribute to the developement of small-scale structures, which are computationally expensive to…

Fluid Dynamics · Physics 2024-12-20 Ciro S. Campolina , Alexei A. Mailybaev

In the quest for advanced propulsion and power-generation systems, high-fidelity simulations are too computationally expensive to survey the desired design space, and a new design methodology is needed that combines engineering physics,…

Reduced models for free-surface flows are required due to the high dimensionality of the underlying incompressible Navier-Stokes equations, which need to fully resolve the flow in vertical direction to compute the surface height. On the…

Numerical Analysis · Mathematics 2025-08-06 Ullika Scholz , Julian Koellermeier

We present a spectral element solver for the steady incompressible Navier-Stokes equations subject to a free surface. Utilizing the kinematic behaviour of the free surface boundary, an iterative pseudo-time procedure is proposed to…

Numerical Analysis · Mathematics 2025-12-30 Simone Minniti , Jens Visbech , Claes Eskilsson , Nicola Parolini , Allan Peter Engsig-Karup

Computational fluid dynamics (CFD) has become a cornerstone of modern water engineering, providing quantitative tools for the analysis, prediction, and management of complex hydraulic systems across a wide range of spatial and temporal…

Fluid Dynamics · Physics 2025-12-19 Anshu Kumar , Kemi Olimba , Vyacheslav Kungurtsev , Fabio V. Difonzo

Hydro-mechanical processes in rough fractures are highly non-linear and govern productivity and associated risks in a wide range of reservoir engineering problems. To enable high-resolution simulations of hydro-mechanical processes in…

In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…

Numerical Analysis · Mathematics 2021-10-12 Amine Hanini , Abdelaziz Beljadid , Driss Ouazar

Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking/capturing of dynamic interfaces between different materials on larger scales.…

Computational Physics · Physics 2018-08-03 Zhijie Xu , Paul Meakin , Alexandre Tartakovsky

Numerical models have long been used to understand geoscientific phenomena, including tidal currents, crucial for renewable energy production and coastal engineering. However, their computational cost hinders generating data of varying…

Computer Vision and Pattern Recognition · Computer Science 2024-02-01 Dongheon Lee , Seungmyong Jeong , Youngmin Ro

We introduce SurfFlow, an open-source high-throughput workflow package designed for automated first-principles calculations of surface energies in arbitrary crystals. Our package offers a comprehensive solution capable of handling…

Materials Science · Physics 2023-11-07 Firat Yalcin , Michael Wolloch

Modeling subsurface fluid flow in porous media is crucial for applications such as oil and gas exploration. However, the inherent heterogeneity and multi-scale characteristics of these systems pose significant challenges in accurately…

Fluid Dynamics · Physics 2026-03-04 Jie Chen , Peiqi Li , Zhengkang He , Simon Hands

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…