Discrétisation d'ordre élevée par des schémas de distribution de résidus

These thesis review some recent results on the construction of very high order multidimensional upwind schemes for the solution of steady and unsteady conservation laws on unstructured triangular grids.We also consider the extension to the approximation of solutions to conservation laws containing second order dissipative terms. To build this high order schemes we use a subtriangulation of the triangular Pk elements where we apply the distribution used for a P1 element.This manuscript is divided in two parts. The first part is dedicated to the design of the high order schemes for scalar equations and focus more on the theoretical design of the schemes. The second part deals with the extension to system of equations, in particular we will compare the performances of 2nd, 3rd and 4th order schemes.The first part is subdivided in four chapters:The aim of the second chapter is to present the multidimensional upwind residual distributive schemes and to explain what was the status of their development at the beginning of this work.The third chapter is dedicated to the first contribution: the design of 3rd and 4th order quasi non-oscillatory schemes.The fourth chapter is composed of two parts: we start by understanding the non-uniformity of the accuracy of the 2nd order schemes for advection-diffusion problem. To solve this issue we use a Finite Element hybridisation.This deep study of the 2nd order scheme is used as a basis to design a 3rd order scheme for advection-diffusion.Finally, in the fifth chapter we extend the high order quasi non-oscillatory schemes to unsteady problems.In the second part, we extend the schemes of the first part to systems of equations as follows:The sixth chapter deals with the extension to steady systems of hyperbolic equations. In particular, we discuss how to solve some issues such as boundary conditions and the discretisation of curved geometries.Then, we look at the performance of 2nd and 3rd order schemes on viscous flow.Finally, we test the space-time schemes on several test cases. In particular, we will test the monotonicity of the space-time non-oscillatory schemes and we apply residual distributive schemes to acoustic problems.Doctorat en Sciences de l'ingénieurinfo:eu-repo/semantics/nonPublishe

Discrétisation d'ordre élevée par des schémas de distribution de résidus

These thesis review some recent results on the construction of very high order multidimensional upwind schemes for the solution of steady and unsteady conservation laws on unstructured triangular grids.We also consider the extension to the approximation of solutions to conservation laws containing second order dissipative terms. To build this high order schemes we use a subtriangulation of the triangular Pk elements where we apply the distribution used for a P1 element.This manuscript is divided in two parts. The first part is dedicated to the design of the high order schemes for scalar equations and focus more on the theoretical design of the schemes. The second part deals with the extension to system of equations, in particular we will compare the performances of 2nd, 3rd and 4th order schemes.The first part is subdivided in four chapters:The aim of the second chapter is to present the multidimensional upwind residual distributive schemes and to explain what was the status of their development at the beginning of this work.The third chapter is dedicated to the first contribution: the design of 3rd and 4th order quasi non-oscillatory schemes.The fourth chapter is composed of two parts: we start by understanding the non-uniformity of the accuracy of the 2nd order schemes for advection-diffusion problem. To solve this issue we use a Finite Element hybridisation.This deep study of the 2nd order scheme is used as a basis to design a 3rd order scheme for advection-diffusion.Finally, in the fifth chapter we extend the high order quasi non-oscillatory schemes to unsteady problems.In the second part, we extend the schemes of the first part to systems of equations as follows:The sixth chapter deals with the extension to steady systems of hyperbolic equations. In particular, we discuss how to solve some issues such as boundary conditions and the discretisation of curved geometries.Then, we look at the performance of 2nd and 3rd order schemes on viscous flow.Finally, we test the space-time schemes on several test cases. In particular, we will test the monotonicity of the space-time non-oscillatory schemes and we apply residual distributive schemes to acoustic problems.Doctorat en Sciences de l'ingénieurinfo:eu-repo/semantics/nonPublishe

Third order residual distribution schemes for the Navier-Stokes equations

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Bayesian-based method with metamodels for rebuilding freestream conditions in atmospheric entry flows

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JAGUAR: a New CFD Code Dedicated to Massively Parallel High-Order LES Computations on Complex Geometry

International audienceLES of industrial flows is associated with geometrical complexity and requires high order schemes to minimize dissipation and dispersion. To tackle these two issues it is necessary to use unstructured grids and High Performance Computing algorithms. In this context, CERFACS initiated two years ago the development of a new CFD code called JAGUAR based on a mathematical framework leading to high-level capability for LES. In this paper, many topics for HPC are introduced and solved in order to obtain the best code performance

Quantification of uncertainty on the catalytic property of reusable thermal protection materials from high enthalpy experiments

An accurate determination of the catalytic property of thermal protection materi- als is crucial to design reusable atmospheric entry vehicles. This property is deter- mined by combining experimental measurements and simulations of the reactive boundary layer near the material surface. The inductively-driven Plasmatron fa- cility at the von Karman Institute for Fluid Dynamics provides a test environment to analyze gas-surface interactions under effective hypersonic conditions. In this study, we develop an uncertainty quantification methodology to rebuild values of the gas enthalpy and material catalytic property from Plasmatron experiments. A non-intrusive spectral projection method is coupled with an in-house boundary- layer solver, to propagate uncertainties and provide error bars on the rebuilt gas enthalpy and material catalytic property, as well as to determine which uncer- tainties have the largest contribution to the outputs of the experiments. We show that the uncertainties computed with the methodology developed are significantly reduced compared to those determined using a more conservative engineering ap- proach adopted in the analysis of previous experimental campaigns

JAGUAR: a New CFD Code Dedicated to Massively Parallel High-Order LES Computations on Complex Geometry

International audienceLES of industrial flows is associated with geometrical complexity and requires high order schemes to minimize dissipation and dispersion. To tackle these two issues it is necessary to use unstructured grids and High Performance Computing algorithms. In this context, CERFACS initiated two years ago the development of a new CFD code called JAGUAR based on a mathematical framework leading to high-level capability for LES. In this paper, many topics for HPC are introduced and solved in order to obtain the best code performance

Comparison of Various CFD Codes for LES Simulations of Turbomachinery: From Inviscid Vortex Convection to Multi-Stage Compressor

peer reviewedSome possible future High Fidelity CFD codes for LES simulation of turbomachinery are compared on several test cases increasing in complexity, starting from a very simple inviscid Vortex Convection to a multistage axial experimental compressor. Simulations were performed between 2013 and 2016 by major Safran partners (Cenaero, Cerfacs, CORIA and Onera) and various numerical methods compared: Finite Volume, Discontinuous Galerkin, Spectral Differences. Comparison to analytical results, to experimental data or to RANS simulations are performed to check and measure accuracy. CPU efficiency versus accuracy are also presented. It clearly appears that the level of maturity could be different between codes and numerical approaches. In the end, advantages and disadvantages of every codes obtained during this project are presented