An immersed body methodology for inviscid flows on Cartesian grids

A preliminary analysis of turbine design, fit for pulsed flow, is proposed in this paper. It focuses on an academic 2D configuration using inviscid flows, since pressure loads due to wave propagation are several orders of magnitude higher than friction and viscous effects do not significantly impinge on the inviscid part, as previously shown by Hermet, 2021. As such, a large parametric study was carried out using the design of experiments methodology. A performance indicator adapted to unsteady environment is carefully defined before detailing the factors chosen for the design of experiments. Since the number of factors is substantial, a screening design to identify the factors influence on the output is first established. The non-influential factors are then omitted in a more quantitative study of the output law. The surface response calculation allows determining the factor level favouring the best output. Consequently, the main trends in the turbine design driven by a pulsed flow can be stated.

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Convergence and Superconvergence of the Local Discontinuous Galerkin Method for Semilinear Second-Order Elliptic Problems on Cartesian Grids

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-021-00123-8 ◽

2021 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Elliptic Problems ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

Cartesian Grids ◽

Local Discontinuous Galerkin ◽

Convergence And Superconvergence ◽

Second Order Elliptic Problems

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An improved Immersed Boundary Method for turbulent flow simulations on Cartesian grids

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110240 ◽

2021 ◽

pp. 110240

Author(s):

Benjamin Constant ◽

Stéphanie Péron ◽

Héloïse Beaugendre ◽

Christophe Benoit

Keyword(s):

Turbulent Flow ◽

Immersed Boundary Method ◽

Immersed Boundary ◽

Cartesian Grids ◽

Flow Simulations ◽

Boundary Method

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On the application of the Kelvin–Arnol'd energy principle to the stability of forced two-dimensional inviscid flows

Journal of Fluid Mechanics ◽

10.1017/s0022112097007854 ◽

1998 ◽

Vol 356 ◽

pp. 221-257 ◽

Cited By ~ 5

Author(s):

P. A. DAVIDSON

Keyword(s):

Magnetic Field ◽

Nonlinear Stability ◽

Broad Class ◽

Mhd Flow ◽

Two Dimensional ◽

Energy Principle ◽

Inviscid Flows ◽

Virtual Displacement ◽

Euler Flows ◽

Universal Procedure

Arnol'd developed two distinct yet closely related approaches to the linear stability of Euler flows. One is widely used for two-dimensional flows and involves constructing a conserved functional whose first variation vanishes and whose second variation determines the linear (and nonlinear) stability of the motion. The second method is a refinement of Kelvin's energy principle which states that stable steady Euler flows represent extremums in energy under a virtual displacement of the vorticity field. The conserved-functional (or energy-Casimir) method has been extended by several authors to more complex flows, such as planar MHD flow. In this paper we generalize the Kelvin–Arnol'd energy method to two-dimensional inviscid flows subject to a body force of the form −ϕ∇f. Here ϕ is a materially conserved quantity and f an arbitrary function of position and of ϕ. This encompasses a broad class of conservative flows, such as natural-convection planar and poloidal MHD flow with the magnetic field trapped in the plane of the motion, flows driven by electrostatic forces, swirling recirculating flow, self-gravitating flows and poloidal MHD flow subject to an azimuthal magnetic field. We show that stable steady motions represent extremums in energy under a virtual displacement of ϕ and of the vorticity field. That is, d1E=0 at equilibrium and whenever d2E is positive or negative definite the flow is (linearly) stable. We also show that unstable normal modes must have a spatial structure which satisfies d2E=0. This provides a single stability test for a broad class of flows, and we describe a simple universal procedure for implementing this test. In passing, a new test for linear stability is developed. That is, we demonstrate that stability is ensured (for flows of the type considered here) whenever the Lagrangian of the flow is a maximum under a virtual displacement of the particle trajectories, the displacement being of the type normally associated with Hamilton's principle. A simple universal procedure for applying this test is also given. We apply our general stability criteria to a range of flows and recover some familiar results. We also extend these ideas to flows which are subject to more than one type of body force. For example, a new stability criterion is obtained (without the use of Casimirs) for natural convection in the presence of a magnetic field. Nonlinear stability is also considered. Specifically, we develop a nonlinear stability criterion for planar MHD flows which are subject to isomagnetic perturbations. This differs from previous criteria in that we are able to extend the linear criterion into the nonlinear regime. We also show how to extend the Kelvin–Arnol'd method to finite-amplitude perturbations.

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