1,720,993 research outputs found
Simple and efficient acceleration of existing multigrid algorithms
No full textA simple, robust, and efficient procedure to accelerate multigrid algorithms is discussed in detail. The approach used in this study is based on the BoostConv routine recently proposed by Citro et al. (“Efficient Stabilization and Acceleration of Numerical Simulation of Fluid Flows by Residual Recombination,” Journal of Computational Physics, Vol. 344, 2017, pp. 234–246). The present study starts from the idea that an existing multigrid code can be improved without any coding effort: a simple call to a black-box subroutine is enough to accelerate the iterative procedure. As a consequence, the proposed approach is well suited to be applied in real-life applications where the complexity of numerical codes is quite far from textbook standards. The application of BoostConv to a model problem is presented here. The algorithm is able to reduce the number of iterations required to get the target accuracy without increasing the computational time of the original code. As a consequence, BoostConv can be used on simple models, characterized by few degrees of freedom, or large numerical problems arising from the discretization of three-dimensional problems
Multiple-scale approximation of instabilities in unsteady boundary layers
No full textA general procedure is developed to study the stability of unsteady boundary layers using complex-ray theory. The propagation of small disturbances is described by a high-frequency (optical) approximation similar to the one adopted for wave propagation in nonuniform media. The ray trajectories, formally defined as the characteristic lines of the eikonal equation, are described by a system of first-order differential equations. These lines are complex valued and provide the main contribution to the propagation of the wave (its Green’s function). As an application, we present the analysis of the flow past on an oscillating airfoil. The propagation of a harmonic disturbance inside the boundary layer is considered and some numerical transition-prediction results are discussed
What non-alcoholic fatty liver disease has got to do with obstructive sleep apnoea syndrome and viceversa?
No full textError sensitivity to refinement: a criterion for optimal grid adaptation
No full textMost indicators used for automatic grid refinement are suboptimal, in the sense that they do not really minimize the global solution error. This paper concerns with a new indicator, related to the sensitivity map of global stability problems, suitable for an optimal grid refinement that minimizes the global solution error. The new criterion is derived from the properties of the adjoint operator and provides a map of the sensitivity of the global error (or its estimate) to a local mesh refinement. Examples are presented for both a scalar partial differential equation and for the system of Navier–Stokes equations. In the last case, we also present a grid-adaptation algorithm based on the new estimator and on the (Formula presented.) software that improves the accuracy of the solution of almost two order of magnitude by redistributing the nodes of the initial computational mesh
Short-wave analysis of 3D and 2D instabilities in a driven cavity
No full textThe short-wave asymptotic approximation of inviscid instabilities proposed by Bayly (Phys. Fluids 31, 1988) and Lifschitz \& Hameiri (Phys. Fluids A 3, 1991) is here applied to the dominant (three-dimensional) instability of two-dimensional flow in either an open or a closed driven cavity, and compared to the structural sensitivity obtained by direct-adjoint computation. The comparison shows that the structural sensitivity of the eigenmode is indeed localized around the critical streamline identified by short-wave asymptotics, and that the latter provides a reasonably good expression of even the first unstable eigenvalue at critical Reynolds number. Curiously enough, the same approximation appears also to apply with success to the two-dimensional instability of the same flow, despite the absence of a large spanwise wavenumber to be used as an expansion parameter. The theoretical justification of this extension, and the importance of phase quantization along the trajectory, will be discussed
Hype or Reality: Should Patients with Metabolic Syndrome-related NAFLD be on the Hunter-Gatherer (Paleo) Diet to Decrease Morbidity?
No full textThe current Western diet figures centrally in the pathogenesis of several chronic diseases such as obesity, type 2 diabetes, cardiovascular disease and the emerging major health problem nonalcoholic fatty liver disease, all of them negatively impacting on life expectancy. This type of diet is represented by a high calorie uptake, high glycemic load, high fat and meat intake, as well as increased consumption of fructose. On the contrary, a simplified way of eating healthily by excluding highly-processed foods, is presumed to be the Paleolithic diet (a diet based on vegetables, fruits, nuts, roots, meat, organ meats) which improves insulin resistance, ameliorates dyslipidemia, reduces hypertension and may reduce the risk of age-related diseases. The diet is the foundation of the treatment of obesity- and type 2 diabetes-related nonalcoholic fatty liver disease and a diet similar to those of pre-agricultural societies may be an effective option. To lend sufficient credence to this type of diet, well-designed studies are needed
Error Sensitivity to Refinement: an optimal criterion for adaptive grid refinement
No full textMost indicators used for automatic grid refinement are suboptimal, in the sense that they do not
really minimize the global solution error. This presentation will concern a new indicator, related to
the sensitivity map of global stability problems, suitable for an optimal grid refinement that minimizes
the global solution error. The new criterion is derived from the properties of the adjoint operator and
provides a map of the sensitivity of the global error (or its estimate) to a local mesh refinement
Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow
No full textThe viscous and inviscid linear stability of the incompressible flow past a square open cavity is studied numerically. The analysis shows that the flow first undergoes a steady three-dimensional bifurcation at a critical Reynolds number of 1370. The critical mode is localized inside the cavity and has a flat roll structure with a spanwise wavelength of about 0.47 cavity depths. The adjoint global mode reveals that the instability is most efficiently triggered in the thin region close to the upstream tip of the cavity. The structural sensitivity analysis identifies the wavemaker as the region located inside the cavity and spatially concentrated around a closed orbit. As the flow outside the cavity plays no role in the generation mechanisms leading to the bifurcation, we confirm that an appropriate parameter to describe the critical conditions in open cavity flows is the Reynolds number based on the average velocity between the two upper edges. Stabilization is achieved by a decrease of the total momentum inside the shear layer that drives the core vortex within the cavity. The mechanism of instability is then studied by means of a short-wavelength approximation considering pressureless inviscid modes. The closed streamline related to the maximum inviscid growth rate is found to be the same as that around which the global wavemaker is concentrated. The structural sensitivity field based on direct and adjoint eigenmodes, computed at a Reynolds number far higher than that of the base flow, can predict the critical orbit on which the main instabilities inside the cavity arise. Further, we show that the sub-leading unstable time-dependent modes emerging at supercritical conditions are characterized by a period that is a multiple of the revolution time of Lagrangian particles along the orbit of maximum growth rate. The eigenfrequencies of these modes, computed by global stability analysis, are in very good agreement with the asymptotic results
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