arXiv subjects

Nishant Nangia

Publications and source records attributed to Nishant Nangia.

6 recordsLinked to original sources

arXiv2021

Critique on "Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry"

In this letter, we provide counter-examples to demonstrate that it is possible to retain second-order accuracy using Sakurai et al.'s method, even when different flux boundary conditions are imposed on multiple interfaces that do not conform to the Cartesian grid. We consider both continuous and discontinuous indicator functions in our test problems. Both indicator functions yield a similar convergence rate for the problems considered here. We also find that the order of accuracy results for some of the cases presented in Sakurai et al. are not reproducible. This is demonstrated by re-considering the same one- and two-dimensional Poisson problems solved in Sakurai et al. in this letter. The results shown in this letter demonstrate that the spatial order of accuracy of the flux-based VP approach of Sakurai et al. is between $\mathcal{O}$(1) and $\mathcal{O}$(2), and it depends on the underlying problem/model. The spatial order of accuracy cannot simply be deduced a priori based on the imposed flux values, shapes, or grid-conformity of the interfaces, as concluded in Sakurai et al. Further analysis is required to understand the spatial convergence rate of the flux-based VP method.

math.NA↗

arXiv2020

The inertial sea wave energy converter (ISWEC) technology: device-physics, multiphase modeling and simulations

In this paper we investigate the dynamics of the inertial wave energy converter (ISWEC) device using fully-resolved computational fluid dynamics (CFD) simulations. Originally prototyped by Polytechnic University of Turin, the device consists of a floating, boat-shaped hull that is slack-moored to the sea bed. Internally, a gyroscopic power take off (PTO) unit converts the wave-induced pitch motion of the hull into electrical energy. The CFD model is based on the incompressible Navier-Stokes equations and utilizes the fictitious domain Brinkman penalization technique to couple the device physics and water wave dynamics. A numerical wave tank is used to emulate realistic sea operating conditions. A Froude scaling analysis is performed to enable two- and three-dimensional simulations for a scaled-down (1:20) ISWEC model. It is demonstrated that the scaled-down 2D model is sufficient to accurately simulate the hull's pitching motion and to predict the power generation capability of the converter. A systematic parameter study of the ISWEC is conducted, and its optimal performance in terms of power generation is determined based on the hull and gyroscope control parameters. It is demonstrated that the device achieves peak performance when the gyroscope specifications are chosen based on reactive control theory. It is shown that a proportional control of the PTO control torque is required to generate continuous gyroscope precession effects, without which the device generates no power. In an inertial reference frame, it is demonstrated that the yaw and pitch torques acting on the hull are of the same order of magnitude, informing future design investigations of the ISWEC technology. Further, an energy transfer pathway from the water waves to the hull, the hull to the gyroscope, and the gyroscope to the PTO unit is analytically described and numerically verified.

physics.flu-dyn↗

arXiv2019

A robust incompressible Navier-Stokes solver for high density ratio multiphase flows

This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The algorithm combines the interface capturing level set method with a variable-coefficient incompressible Navier-Stokes solver that is demonstrated to stably resolve material contrast ratios of up to six orders of magnitude. The discretization approach ensures second-order pointwise accuracy for both velocity and pressure with several physical boundary treatments, including velocity and traction boundary conditions. The paper includes several test cases that demonstrate the order of accuracy and algorithmic scalability of the flow solver. To ensure the stability of the numerical scheme in the presence of high density and viscosity ratios, we employ a consistent treatment of mass and momentum transport in the conservative form of discrete equations. This consistency is achieved by solving an additional mass balance equation, which we approximate via a strong stability preserving Runga-Kutta time integrator and by employing the same mass flux (obtained from the mass equation) in the discrete momentum equation. The scheme uses higher-order total variation diminishing (TVD) and convection-boundedness criterion (CBC) satisfying limiter to avoid numerical fluctuations in the transported density field. The high-order bounded convective transport is done on a dimension-by-dimension basis, which makes the scheme simple to implement. We also demonstrate through several test cases that the lack of consistent mass and momentum transport in non-conservative formulations, which are commonly used in practice, or the use of non-CBC satisfying limiters can yield very large numerical error and very poor accuracy for convection-dominant high density ratio flows.

physics.comp-ph↗

arXiv2019

A DLM immersed boundary method based wave-structure interaction solver for high density ratio multiphase flows

We present a robust immersed boundary (IB) method for high density ratio multiphase flows that is capable of modeling complex wave-structure interaction (WSI) problems arising in marine and coastal engineering applications. The IB/WSI methodology is enabled by combining the distributed Lagrange multiplier (DLM) method of Sharma and Patankar (J Comp Phys, 2005) with a robust level set method based multiphase flow solver. The fluid solver integrates the conservative form of the variable-coefficient incompressible Navier-Stokes equations using a hybrid preconditioner and ensures consistent transport of mass and momentum at a discrete level. The consistent transport scheme preserves the numerical stability of the method in the presence of large density ratios found in problems involving air, water, and an immersed structure. The air-water interface is captured by the level set method on an Eulerian grid, whereas the free-surface piercing immersed structure is represented on a Lagrangian mesh. The fluid-structure interaction (FSI) coupling is mediated via Peskin's regularized delta functions in an implicit manner, which obviates the need to integrate the hydrodynamic stress tensor on the complex surface of the immersed structure. The IB/WSI numerical scheme is implemented within an adaptive mesh refinement (AMR) framework, in which the Lagrangian structure and the air-water interface are embedded on the finest mesh level to capture the thin boundary layers and the vortical structures arising from WSI. We use a well-balanced force discretization for gravity force that eliminates spurious velocity currents in the hydrostatic limit due to density variation in the three phases (air, water and solid). An effective wave generation and absorption technique for a numerical wave tank is presented and used to simulate a benchmark case of water wave distortion due to a submerged structure.

physics.flu-dyn↗

arXiv2019

Simulating water-entry/exit problems using Eulerian-Lagrangian and fully-Eulerian fictitious domain methods within the open-source IBAMR library

In this paper we employ two implementations of the fictitious domain (FD) method to simulate water-entry and water-exit problems and demonstrate their ability to simulate practical marine engineering problems. In FD methods, the fluid momentum equation is extended within the solid domain using an additional body force that constrains the structure velocity to be that of a rigid body. Using this formulation, a single set of equations is solved over the entire computational domain. The constraint force is calculated in two distinct ways: one using an Eulerian-Lagrangian framework of the immersed boundary (IB) method and another using a fully-Eulerian approach of the Brinkman penalization (BP) method. Both FSI strategies use the same multiphase flow algorithm that solves the discrete incompressible Navier-Stokes system in conservative form. A consistent transport scheme is employed to advect mass and momentum in the domain, which ensures numerical stability of high density ratio multiphase flows involved in practical marine engineering applications. Example cases of a free falling wedge (straight and inclined) and cylinder are simulated, and the numerical results are compared against benchmark cases in literature.

math.NA↗

arXiv2017

A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

We present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid-structure interface are avoided and far-field (smooth) velocity and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torques through force/torque balance equation in a Lagrangian frame that some of us took in a prior work (Bhalla et al., J Comp Phys, 2013). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods.

math.NA↗