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Advances in Applied Mathematics and Mechanics 2021年第1期13卷 119-139页

作者： Mohamed Kara Salim Mesbahi Philippe Angot Applied Mathematics Laboratory Department of MathematicsFaculty of SciencesFerhat Abbas UniversitySetifAlgeria Fundamental and Numerical Mathematics Laboratory Department of MathematicsFaculty of SciencesFerhat Abbas UniversitySetifAlgeria Aix-Marseille Universit´e Institut de Math´ematiques de MarseilleCNRS UMR 7373MarseilleFrance

In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume *** main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious ***,we present a cell-centered finite volume method to discretize the fictitious domain *** proposed method is numerically validated for different test *** work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.

关键词： Fictitious domain method sharp interface elasticity system jump embedded boundary conditions finite volume method

A sharp-interface immersed boundary method for simulating high-speed compressible inviscid flows

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Advances in Aerodynamics 2020年第1期2卷 455-473页

作者： Junjie Wang Xiangyu Gu Jie Wu Department of Aerodynamics Nanjing University of Aeronautics and AstronauticsNanjing 210016China China Academy of Launch Vehicle Technology Beijing 100076China Key Laboratory of Unsteady Aerodynamics and Flow Control Ministry of Industry and Information TechnologyNanjing University of Aeronautics and AstronauticsNanjing 210016China

This paper presents a robust sharp-interface immersed boundary method for simulating inviscid compressible flows over stationary and moving *** flow field is governed by Euler equations,which are solved by using the open source library *** such as those introduced by shock waves are captured by using Kurganov and Tadmor divergence ***-slip boundary conditions are enforced at the boundary of body through reconstructing flow variables at some ghost *** values are obtained indirectly by interpolating from their mirror points.A bilinear interpolation is employed to determine the variables at the mirror points from boundary conditions and flow conditions around the *** validate the efficiency and accuracy of this method for simulation of high-speed inviscid compressible flows,four cases have been simulated as follows:supersonic flow over a 15°angle wedge,transonic flow past a stationary airfoil,a piston moving with supersonic velocity in a shock tube and a rigid circular cylinder lift-off from a flat surface triggered by a shock *** to the exact analytical solutions or the results in literature,good agreement can be achieved.

关键词： Immersed boundary method Inviscid compressible flows sharp interface Shock waves OpenFOAM

A Hybrid Scheme of Level Set and Diffuse interface Methods for Simulating Multi-Phase Compressible Flows

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Numerical Mathematics(Theory,Methods and Applications) 2022年第3期15卷 715-743页

作者： Meiyan Fu Tiao Lu School of Mathematical Sciences Peking UniversityBeijingChina Northwest Institute of Nuclear Technology Xi’anChina HEDPS&CAPT LMAM&School of Mathematical SciencesPeking UniversityBeijingChina

We propose a hybrid scheme combing the level set method and the multicomponent diffuse interface method to simulate complex multi-phase *** overall numerical scheme is based on a sharp interface framework where the level set method is adopted to capture the material interface,the Euler equation is used to describe a single-phase flow on one side of the interface and the six-equation diffuse interface model is applied to model the multi-phase mixture or gas-liquid cavitation on the other *** exact Riemann solver,between the Euler equation and the six-equation model with highly nonlinear Mie-Gr¨uneisen equations of state,is developed to predict the interfacial states and compute the phase interface *** numerical examples,including shock tube problems,cavitation problems,air blast and underwater explosion applications are presented to validate the numerical scheme and the Riemann solver.

关键词： Multi-phase flow sharp interface diffuse interface level set six-equation model exact Riemann solver Mie-Gruneisen equation of state

Modeling of the Saltwater Intrusion Using the Level Set Method. Application to Henry’s Problem

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Computational Water, Energy, and Environmental Engineering 2022年第1期11卷 11-33页

作者： Joachna Meya Loua-Bouayi Christian Tathy Adolphe Kimbonguila Manounou Laboratoire Mécanique Energétique et Ingénierie Ecole Nationale Supérieure Polytechnique Université Marien Ngouabi Brazzaville Congo

The salt intrusion phenomenon is caused by overexploitation of aquifers in coastal areas. This physical phenomenon has been the subject of numerous studies and numerous methods have been proposed, with the aim of protecting the quality of the water in these aquifers. This work proposes a two-dimensional saline intrusion model using the sharp interface approach and the level set method. It consists of a parabolic equation modeling the underground flow and a hyperbolic Equation (the level set equation) which makes it possible to track the evolution of the interface. High-order numerical schemes such as the space scheme WENO5 and the third-order time scheme TVD-RK were used for the numerical resolution of the hyperbolic equation. To limit the tightening of the contour curves of the level set function, the redistanciation or reinitialization algorithm proposed by Su

关键词： Confined Aquifer Seawater Intrusion Level Set Method sharp interface Henry Problem