Sanjay R. Mathur

A Reynolds-averaged Navier-Stokes solver using unstructured mesh-based finite-volume scheme

A Reynolds-Averaged Navier-Stokes (RANS) solver for unstructured meshes is presented and validated for a number of turbulent flows. The RANS solver employs a cellcentered, second-order accurate finite-volume discretization based on linear reconstruction, in conjunction with a pressure-based segregated solution procedure, k-e models are used for turbulence closure with wall functions. Quadrilateral and triangular meshes with or without local refinement are employed in the validations. It is demonstrated that the proposed solver can predict the selected flows with good accuracy, and that the quality of the predictions is comparable to that of structured mesh based solvers. It is also shown that local mesh adaptation provides an economical means of resolving the critical regions of the flow.

An Unstructured Finite-Volume Method for Incompressible Flows with Complex Immersed Boundaries

A numerical method is developed for solving three-dimensional, unsteady, incompressible flows with immersed moving solids of arbitrary geometric complexity. A co-located (nonstaggered) pressure-based finite-volume method is employed to solve the Navier-Stokes equations for the flow region, and the solid region is represented by material points with known position and velocity. The influence of the body on the flow is accounted for by reconstructing implicitly the velocity on the immersed boundary faces b-tween fluid and solid. Canonical test cases and mesh convergence tests are carried out. A validation test for the vibration of microcantilevers shows good agreement between computed and measured damping factor values.

An Unstructured Finite-Volume Method for Structure–Electrostatics Interactions in MEMS

Radio-frequency microelectromechanical systems (RF MEMS) are widely used for contact actuators and capacitive switches, and involve metal–dielectric contact. In these devices, the structure is activated by an electrostatic force, whose magnitude changes as the gap closes. It is advantageous to model fluid and structural mechanics and electrostatics within a single comprehensive numerical framework to facilitate coupling between them. In this article, we extend a cell-based finite-volume approach popularly used to simulate fluid flow to characterize structure–electrostatics interactions. The method employs fully implicit second-order finite-volume discretization of the integral conservation equations governing elastic solid mechanics and electrostatics, and uses arbitrary convex polyhedral meshes. Results are presented in this article for a fixed-fixed beam under electrostatic actuation.

Finite-Volume Method for Structural Analysis of RF MEMS Devices Using the Theory of Plates

Radio-frequency microelectromechanical systems (RF MEMS) have wide applicability in contact actuators and capacitive switches. In these devices, the membrane deforms under nonlinearly varying electrostatic actuation. It is advantageous to adopt a single comprehensive numerical framework to model these coupled systems. Frequently, the membranes are very thin with aspect ratios as high as 1:500. We model these membranes using the theory of plates and make use of the Mindlin-Reissner plate theory. In this article, we describe a cell-centered finite-volume approach to discretize the governing equations. Transverse deflection and bending moment distributions are first described for canonical test problems, verifying the accuracy of the method. Results are then presented for a fixed-fixed MEMS device, modeled as a thin plate, under electrostatic actuation.

Computational Heat Transfer in Complex Systems: A Review of Needs and Opportunities

During the few decades, computational techniques for simulating heat transfer in complex industrial systems have reached maturity. Combined with increasingly sophisticated modeling of turbulence, chemistry, radiation, phase change, and other physics, powerful computational fluid dynamics (CFD) and computational heat transfer (CHT) solvers have been developed which are beginning to enter the industrial design cycle. In this paper, an overview of emerging simulation needs is first given, and currently-available CFD techniques are evaluated in light of these needs. Emerging computational methods which address some of the failings of current techniques are then reviewed. New research opportunities for computational heat transfer, such as in submicron and multiscale heat transport, are reviewed. As computational techniques and physical models become mature, there is increasing demand for predictive simulation, that is, simulation which is not only verified and validated, but whose uncertainty is also quantified. Current work in the area of sensitivity computation and uncertainty propagation is described.

Numerical Schemes for the Convection-Diffusion Equation Using a Meshless Finite-Difference Method

A meshless finite-difference method is developed for solving the steady convection-diffusion equation. A weighted least-squares procedure is used to compute a local polynomial fit which is used to find the derivatives appearing in the governing partial differential equation. A number of upwind-weighted discretization schemes for the convective operator are developed, analogous to traditional finite-difference schemes. These include a first-order upwind and a second-order upwind scheme, as well as a new scheme, the minimum gradient scheme, analogous to the essentially nonoscillatory (ENO) scheme. The order of accuracy of these methods is studied by applying them to two test problems. The first is the convection and diffusion of a scalar in a uniform velocity field, and the second pertains to scalar transport in a vortical flow field. The first-order upwind scheme results in an oscillation-free solution across the range of Peclet numbers and displays an order of accuracy close to unity. The second-order upwind scheme results in spurious oscillations for coarse nonuniform point distributions for Peclet numbers greater than 2.0, but monotonic solutions are obtained for finer point distributions across the range of Peclet numbers. The minimum gradient scheme yields nonoscillatory solutions for all Peclet numbers and point distributions explored in this work.

Finite-Volume Method for Creep Analysis of Thin RF MEMS Devices Using the Theory of Plates

Creep is a critical physical mechanism responsible for the failure of radio-frequency (RF) capacitive micro-electro-mechanical systems (MEMS) switches, especially those operating at high RF power. Accurate modeling of creep in RF MEMS metallic membranes is necessary to estimate device lifetime and to improve their reliability. Moreover, the devices are frequently very thin, with aspect ratios as high as 1:500, and conventional three-dimensional structural modeling is onerous and unnecessary. In this article we extend a cell-centered finite-volume approach, previously developed to model thin membranes using Mindlin-Reissner plate theory, to study creep in RF MEMS devices. Results show that the present methodology can accurately predict the long-term creep behavior in thin RF MEMS devices in a computationally efficient manner.

Application of the Immersed Boundary Method to Fluid, Structure, and Electrostatics Interaction in MEMS

A comprehensive computational model is developed to study the dynamics of electrostatically actuated micro-electro-mechanical system (MEMS) switches. The operation of the device involves a coupled interaction of structure response, fluid dynamics and electrostatics. A unified computational framework based on the finite volume method (FVM) is developed to account for these mechanisms. The coupling between the multiple physics is achieved by employing the immersed boundary method (IBM). This computational tool is applied to study the pull-in phenomena of a variety of MEMS devices, including fix-fix beam, cantilever and frog-leg.

An Acceleration Technique for the Computation of Participating Radiative Heat Transfer

It is known that the finite volume and discrete ordinates methods for computing participating radiation are slow to converge when the optical thickness of the medium becomes large. This is a result of the sequential solution procedure usually employed to solve the directional intensities, which couples the ordinate directions and the energy equation loosely. Previously published acceleration techniques have sought to employ a governing equation for the angular-average of the radiation intensity to promote inter-directional coupling. These techniques have not always been successful, and even where successful, have been found to destroy the conservation properties of the radiative transfer equation. In this paper, we develop an algorithm called Multigrid Acceleration using Global Intensity Correction (MAGIC) which employs a multigrid solution of the average intensity and energy equations to significantly accelerate convergence, while ensuring that the conservative property of the radiative transfer equation is preserved. The method is shown to perform well for radiation heat transfer problems in absorbing, emitting and scattering media, both and without radiative equilibrium, and across a range of optical thicknesses.Copyright

A Unified Unintrusive Discrete Approach to Sensitivity Analysis and Uncertainty Propagation in Fluid Flow Simulations

In recent years, there has been growing interest in making computational fluid dynamics (CFD) predictions with quantifiable uncertainty. Tangent-mode sensitivity analysis and uncertainty propagation are integral components of the uncertainty quantification process. Generalized polynomial chaos (gPC) is a viable candidate for uncertainty propagation, and involves representing the dependant variables in the governing partial differential equations (pdes) as expansions in an orthogonal polynomial basis in the random variables. Deterministic coupled non-linear pdes are derived for the coefficients of the expansion, which are then solved using standard techniques. A significant drawback of this approach is its intrusiveness. In this paper, we develop a unified approach to automatic code differentiation and Galerkin-based gPC in a new finite volume solver, MEMOSA-FVM, written in C++. We exploit templating and operator overloading to perform standard mathematical operations, which are overloaded either to perform code differentiation or to address operations on polynomial expansions. The resulting solver is capable of either performing sensitivity or uncertainty propagation, with the choice being made at compile time. It is easy to read, looks like a deterministic CFD code, and can address new classes of physics automatically, without extensive re-implementation of either sensitivity or gPC equations. We perform tangent (forward) mode sensitivity analysis and Galerkin gPC-based uncertainty propagation in a variety of problems, and demonstrate the effectiveness of this approach.Copyright