Finite volume and finite element schemes for the euler equations in cylindrical and spherical coordinates

A numerical scheme is presented for the solution of the compressible Euler equations over unstructured grids in cylindrical and spherical coordinates. The proposed scheme is based on a mixed finite volume / finite element approach. Numerical simulations are presented for the explosion problem in two spatial dimensions in cylindrical and spherical coordinates, and the numerical results are compared with the one-dimensional simulation for cylindrically and spherically symmetric explosions

Decomposition of high-order statistics

ANOVA analysis is a very common numerical technique for computing a hierarchy of most important input parameters for a given output when variations are computed in terms of variance. This second central moment can not be retained as an universal criterion for ranking some variables, since a non-gaussian output could require higher order (more than second) statistics for a complete description and analysis. In this work, we illustrate how third and fourth-order statistic moments, \textit{i.e.} skewness and kurtosis, respectively, can be decomposed. It is shown that this decomposition is correlated to a polynomial chaos expansion, permitting to easily compute each term. Then, new sensitivity indices are proposed basing on the computation of the kurtosis. An analytical example is provided with the explicit computation of the variance and the skewness. Some test-cases are introduced showing the importance of ranking the kurtosis too

Non-polynomial expansion for stochastic problems with non-classical pdfs

In this study, some preliminary results about the possibility to extend the classical polynomial Chaos (PC) theory to stochastic problems with non-classical probability distributions of the variables, i.e. outside the framework of the classical Wiener-Askey scheme, are presented. The proposed strategy allows to obtain an analytical representation of the solution in order to build a metamodel or to compure conditional statistics. Various numerical results obtained on some analytical problems are then provided to demonstrate the correctness of the presented approach

Throughput Analysis of IEEE 802.11bn Coordinated Spatial Reuse

Multi-Access Point Coordination (MAPC) is becoming the cornerstone of the IEEE 802.11bn amendment, alias Wi-Fi 8. Among the MAPC features, Coordinated Spatial Reuse (C-SR) stands as one of the most appealing due to its capability to orchestrate simultaneous access point transmissions at a low implementation complexity. In this paper, we contribute to the understanding of C-SR by introducing an analytical model based on Continuous Time Markov Chains (CTMCs) to characterize its throughput and spatial efficiency. Applying the proposed model to several network topologies, we show that C-SR opportunistically enables parallel high-quality transmissions and yields an average throughput gain of up to 59% in comparison to the legacy 802.11 Distributed Coordination Function (DCF) and up to 42% when compared to the 802.11ax Overlapping Basic Service Set Packet Detect (OBSS/PD) mechanism

A One-Time Truncate and Encode Multiresolution Stochastic Framework

In this work a novel adaptive strategy for stochastic problems, inspired to the classical Harten's framework, is presented. The proposed algorithm allows building, in a very general manner, stochastic numerical schemes starting from a whatever type of deterministic schemes and handling a large class of problems, from unsteady to discontinuous solutions. Its formulations permits to recover the same results concerning the interpolation theory of the classical multiresolution approach, but with an extension to uncertainty quantification problems. The interest of the present strategy is demonstrated by performing several numerical problems where different forms of uncertainty distributions are taken into account, such as discontinuous and unsteady custom-defined probability density functions. In addition to algebraic and ordinary differential equations, numerical results for the challenging 1D Kraichnan-Orszag are reported in terms of accuracy and convergence. Finally, a two degree-of-freedom aeroelastic model for a subsonic case is presented. Though quite simple, the model allows recovering some physical key aspect, on the fluid/structure interaction, thanks to the quasi-steady aerodynamic approximation employed. The injection of an uncertainty is chosen in order to obtain a complete parameterization of the mass matrix. All the numerical results are compared with respect to classical Monte Carlo solution and with a non-intrusive Polynomial Chaos method