https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Fri, 15 May 2026 22:55:43 GMT 2026-05-15T22:55:43Z http://hdl.handle.net/10985/18046 A Higher-Order Chimera Method for Finite Volume Schemes RAMÍREZ, Luis; NOGUEIRA, Xesús; OURO, Pablo; NAVARRINA, Fermín; COLOMINAS, Ignasi; KHELLADI, Sofiane In this work a higher-order accurate finite volume method for the resolution of the Euler/Navier–Stokes equations using Chimera grid techniques is presented. The formulation is based on the use of Moving Least Squares approximations in order to obtain higher-order accurate reconstruction and connectivity between the overlapped grids. The accuracy and performance of the proposed methodology is demonstrated by solving different benchmark problems. Sun, 01 Jan 2017 00:00:00 GMT http://hdl.handle.net/10985/18046 2017-01-01T00:00:00Z RAMÍREZ, Luis NOGUEIRA, Xesús OURO, Pablo NAVARRINA, Fermín COLOMINAS, Ignasi KHELLADI, Sofiane In this work a higher-order accurate finite volume method for the resolution of the Euler/Navier–Stokes equations using Chimera grid techniques is presented. The formulation is based on the use of Moving Least Squares approximations in order to obtain higher-order accurate reconstruction and connectivity between the overlapped grids. The accuracy and performance of the proposed methodology is demonstrated by solving different benchmark problems. http://hdl.handle.net/10985/18007 A high-order finite volume method with improved isotherms reconstruction for the computation of multiphase flows using the Navier–Stokes–Korteweg equations MARTÍNEZ, Abel; RAMÍREZ, Luis; NOGUEIRA, Xesús; KHELLADI, Sofiane; NAVARRINA, Fermín In this work we solve the Navier–Stokes–Korteweg (NSK) equations to simulate a two-phase fluid with phase change. We use these equations on a diffuse interface approach, where the properties of the fluid vary continuously across the interface that separates the different phases. The model is able to describe the behavior of both phases with the same set of equations, and it is also able to handle problems with great changes in the topology of the problem. However, high-order derivatives are present in NSK equations, which is a difficulty for the design of a numerical method to solve the problem. Here, we propose the use of a high-order Finite Volume method with Moving Least Squares approximations to handle high-order derivatives and solve the NSK equations. Moreover, a new methodology to obtain accurate equations of state is presented. In this method, we use any accurate equation of state for the pure phases. Under the saturation curve, a B-spline reconstruction fulfilling a given set of thermodynamic criteria is performed. The new EOS can be used for computations using diffuse interface modeling. Several numerical examples to show the accuracy of the new approach are presented. Wed, 01 Jan 2020 00:00:00 GMT http://hdl.handle.net/10985/18007 2020-01-01T00:00:00Z MARTÍNEZ, Abel RAMÍREZ, Luis NOGUEIRA, Xesús KHELLADI, Sofiane NAVARRINA, Fermín In this work we solve the Navier–Stokes–Korteweg (NSK) equations to simulate a two-phase fluid with phase change. We use these equations on a diffuse interface approach, where the properties of the fluid vary continuously across the interface that separates the different phases. The model is able to describe the behavior of both phases with the same set of equations, and it is also able to handle problems with great changes in the topology of the problem. However, high-order derivatives are present in NSK equations, which is a difficulty for the design of a numerical method to solve the problem. Here, we propose the use of a high-order Finite Volume method with Moving Least Squares approximations to handle high-order derivatives and solve the NSK equations. Moreover, a new methodology to obtain accurate equations of state is presented. In this method, we use any accurate equation of state for the pure phases. Under the saturation curve, a B-spline reconstruction fulfilling a given set of thermodynamic criteria is performed. The new EOS can be used for computations using diffuse interface modeling. Several numerical examples to show the accuracy of the new approach are presented. http://hdl.handle.net/10985/18002 An a posteriori-implicit turbulent model with automatic dissipation adjustment for Large Eddy Simulation of compressible flows NOGUEIRA, Xesús; RAMÍREZ, Luis; FERNÁNDEZ-FIDALGO, Javier; DELIGANT, Michael; KHELLADI, Sofiane; CHASSAING, Jean-Camille; NAVARRINA, Fermín In this work we present an a posteriori high-order finite volume scheme for the computation of compressible turbulent flows. An automatic dissipation adjustment (ADA) method is combined with the a posteriori paradigm, in order to obtain an implicit subgrid scale model and preserve the stability of the numerical method. Thus, the numerical scheme is designed to increase the dissipation in the control volumes where the flow is under-resolved, and to decrease the dissipation in those cells where there is excessive dissipation. This is achieved by adding a multiplicative factor to the dissipative part of the numerical flux. In order to keep the stability of the numerical scheme, the a posteriori approach is used. It allows to increase the dissipation quickly in cells near shocks if required, ensuring the stability of the scheme. Some numerical tests are performed to highlight the accuracy and robustness of the proposed numerical scheme. Wed, 01 Jan 2020 00:00:00 GMT http://hdl.handle.net/10985/18002 2020-01-01T00:00:00Z NOGUEIRA, Xesús RAMÍREZ, Luis FERNÁNDEZ-FIDALGO, Javier DELIGANT, Michael KHELLADI, Sofiane CHASSAING, Jean-Camille NAVARRINA, Fermín In this work we present an a posteriori high-order finite volume scheme for the computation of compressible turbulent flows. An automatic dissipation adjustment (ADA) method is combined with the a posteriori paradigm, in order to obtain an implicit subgrid scale model and preserve the stability of the numerical method. Thus, the numerical scheme is designed to increase the dissipation in the control volumes where the flow is under-resolved, and to decrease the dissipation in those cells where there is excessive dissipation. This is achieved by adding a multiplicative factor to the dissipative part of the numerical flux. In order to keep the stability of the numerical scheme, the a posteriori approach is used. It allows to increase the dissipation quickly in cells near shocks if required, ensuring the stability of the scheme. Some numerical tests are performed to highlight the accuracy and robustness of the proposed numerical scheme.