Search

We construct a third order multidimensional upwind residual distribution scheme for the system of the Navier–Stokes equations. The underlying approximation is obtained using standard P2 Lagrange finite elements. To discretise the inviscid component of the equations, each element is divided in sub-elements over which we compute a high order residual defined as the integral of the inviscid fluxes on the boundary of the sub-element. The residuals are distributed to the nodes of each sub-element in a multi-dimensional upwind way. To obtain a discretisation of the viscous terms consistent with this multi-dimensional upwind approach, we make use of a Petrov–Galerkin analogy. The analogy allows to find a family of test functions which can be used to obtain a weak approximation of the viscous terms. The performance of this high-order method is tested on flows with high and low Reynolds number.

This article deals with the discretization of linearized Euler equations by multidimensional upwind residual distribution methods. Linearized Euler equations are applied to model the propagation of sound in the domain where no source of sound is present and where the analogy methods such as Ffowcs―Williams can not be used because of gradients in the mean flow. The residual distribution method leads to a class of schemes that shares properties of both finite element method and finite volume method. In particular, the schemes used here are multidimensional upwind, which make them very attractive because of their low cross-dissipation. First, the discretization method is introduced as an alternative method for computational aeroacoustic applications on unstructured grids. The residual distribution method is then analyzed analytically for wave propagation. Next it is applied to linearized Euler equations with proper acoustic boundary conditions, and finally verifiedon test cases having exact solution.

Residual distribution schemes on curved geometries are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution, defined by a Finite Element space based on triangular Lagrangian Pk elements, is globally continuous. A natural sub-triangulation of these elements allows to reuse the simple distribution schemes previously developed for linear P1 triangles. The paper introduces curved elements with piecewise quadratic and cubic approximation of the boundaries of the domain, using standard sub- or isoparametric transformation. Numerical results for the Euler equations confirm the predicted order of accuracy, showing the importance of a higher order approximation of the geometry.

The post§ight analysis of a space mission requires accurate determination of the free-stream conditions for the trajectory. The Mach number, temperature, and pressure conditions can be rebuilt from the heat §ux and pressure measured on the spacecraft by means of a Flush Air Data System (FADS). This instrumentation comprises a set of sensors §ush mounted in the thermal protection system to measure the static pressure (pressure taps) and heat §ux (calorimeters). Knowing that ex

Imposing subsonic outlet boundary conditions for compressible ow simulations is still a challenging problem, since spurious re ections are occurring if unsteady disturbances leaving the domain. Most of the non-re ecting boundary conditions can be found in the literature performing very well if only acoustic perturbations are considered, but they are less e ective if there are vortical structures passing through the boundaries. This issue is true for both inlets and outlets, but in the current paper just outlets are considered in 2D and 3D. In the literature these spurious waves due to unsteady perturbation passing though the boundaries are called re ections. However, if a vortical structure is leaving the domain, the acoustic waves propagating back to the solution domain are rather created. In this sense, the original characteristic equations are modi ed such that the source terms responsible for these spurious waves could be identi ed and deactivated. In such a way, the vortical disturbances can pass the boundaries and therefore no more bu er zone is needed. In this paper, we used this approach to design non-re ecting outlet using residual distribution schemes to solve the bulk ow. We have developed the new boundary condition for both Linearized Euler Equations and Navier-Stokes Equations.

boundary conditions are applied for subsonic outlet in order to adjust it to the multidimensional upwind discretization of Residual Distribution Method. The article analyzes boundary conditions from the litera- ture and gives suggestions of improvement based on physical considerations. The dierent formulations are compared through analytical problems.

This article is dedicated to the design of high order residual distributive schemes for unsteady problems. We use a space-time strategy, which means that the time is considered as a third dimension. To achieve high order both in space and in time, we use prismatic elements having (k+1) levels, each level being a P k element. The first section is dedicated to the deign of space-time schemes on such elements. The second section presents the performances on different type of problems. In particular, we look at a discontinuous problem on Euler equations and two problems of propagation of sound using Linearised Euler equations.

This article deals with the discretization of Linearized Euler Equations (LEEs) by multidimensional upwind Residual Distribution methods. Linearized Euler equations are applied in the domain where there is no source of sound and the analogy methods such as Ffowcs-Williams can not be used because of gradients in the mean flow. Residual distribution method is a class of schemes that is in between finite-element and finite-volume. In particular, the schemes that we use are multidimensional upwind which make them very attractive because of their very low cross-dissipation. First, we define the formulation of the LEEs that we choose to use. Then, we focus on the residual schemes and we describe two ways of discretizing unsteady problems. The third part presents a wave number of those schemes. Finally, we show the advantage of these schemes on several acoustic problems.