Sagar Kapadia

Petrov-Galerkin and discontinuous-Galerkin methods for time-domain and frequency-domain electromagnetic simulations

Finite-element discretizations for Maxwells first-order curl equations in both the time domain and frequency domain are developed. Petrov-Galerkin and discontinuous-Galerkin formulations are compared using higher-order basis functions. Verification cases are run to examine the accuracy of the algorithms on problems with exact solutions. Comparisons with other, well accepted, methodologies are also considered for problems for which exact solutions do not exist. Effects of several parameters, including spatial and temporal refinement, are also examined and the relative efficiency of each scheme is discussed. By considering test cases previously considered by other researchers, it is also demonstrated that the algorithms do not exhibit spurious solutions. Finally, three-dimensional results are compared with test results for a rectangular waveguide for which experimental data has been obtained with the explicit purpose of code-validation. The ability to predict changes in scattering parameters caused by variations in geometric and material properties are examined and it is demonstrated that the algorithms predict these changes with good accuracy.

Three-Dimensional Stabilized Finite Elements for Compressible Navier–Stokes

In this paper, a stabilized finite-element approach is used in the development of a high-order flow solver for compressible flows. The streamline/upwind Petrov–Galerkin discretization is used for the Navier–Stokes equations, and a fully implicit methodology is used for advancing the solution at each time step. The order of accuracy is assessed for both inviscid and viscous flows using the method of manufactured solutions. For two-dimensional flow, a mesh-curving strategy is discussed that allows high-aspect-ratio curved elements in viscous flow regions. In addition, the effects of curved elements are evaluated in two dimensions using the method of manufacture solutions. Finally, test cases are presented in two and three dimensions and compared with well-established results and/or experimental data.

High-Order Finite-Element Method for Three-Dimensional Turbulent Navier-Stokes

In this paper a high-order streamline/upwind Petrov-Galerkin (SUPG) finite element discretization is investigated and developed for solutions of three-dimensional turbulent flows. The modified Spalart and Allmaras (SA) turbulence model is implemented and is discretized consistently with the main Reynolds Averaged Navier-Stokes (RANS) equations using the high-order finite element scheme. The present method treats the discretized system fully implicitly to obtain steady state solutions or to drive unsteady problems at each time step. To accurately represent the geometries, high-order curved boundary meshes are generated via a CAPRI interface, while the interior meshes are deformed through a linear elasticity solver. This procedure effectively prevents the generation of collapsed elements due to the projection of the curved physical boundaries and thus allows high-aspect-ratio curved elements in viscous boundary layers. Several numerical examples, including viscous flow over a three-dimensional cylinder and flow over an ONERA M6 swept wing are presented and compared with a discontinuous-Galerkin method. Finally, solutions are obtained for a high-lift multi-element wing to demonstrate the capability of the high-order finite element solver.

High-order Methods for Solutions of Three-dimensional Turbulent Flows

This paper presents a high-order discontinuous Galerkin (DG) method for three-dimensional turbulent flows. As an extension of our previous work, the paper further investigates the incorporation of a modified Spalart-and-Allmaras (SA) turbulence model with the Reynolds Averaged Navier-Stokes (RANS) equations that are both discretized using a modal discontinuous Galerkin approach. The resulting system of equations, describing the conservative flow fields as well as the turbulence variable, is solved implicitly by an approximate Newton approach with a local time-stepping method to alleviate the initial transient effects. In the context of high-order methods, curved surface mesh is generated through the use of a CAPRI mesh parameterization tool, followed by a linear elasticity solver to determine the interior mesh deformations. The requirements for the wall coordinate and viscous stretching factor used for viscous mesh generation are studied on a twodimensional turbulent flow case. It has been concluded that, for attached turbulent flows, the conventional parameters often used in low-order methods can be somewhat less stringent when a higher-order method is considered. Several other numerical examples including a direct numerical simulation of the Taylor-Green vortex and turbulent flow over an ONERA M6 wing are considered to assess the solution accuracy and to show the performance of high-order DG methods in capturing transitional and turbulent flow phenomena.

High-Order Discontinuous Galerkin Method for Computation of Turbulent Flows

This paper presents a high-order discontinuous Galerkin method for computation of compressible turbulent flows in three space dimensions. A modified Spalart-and-Allmaras turbulence model is implemented and discretized to the same order of accuracy as that for the Reynolds-averaged Navier–Stokes equations. The creation of curvilinear meshes for arbitrary three-dimensional configurations is achieved through the aid of a computational analysis programming interface, which enables direct communications with the computer-aided design module to determine the true positions of surface quadrature points for high-order geometric representations. A modified linear elasticity approach is used sequentially and is of crucial importance for reshaping the interior mesh to allow high-aspect-ratio curved elements in turbulent boundary layers. Requirements of the mesh parameters, including the wall spacing and viscous stretching factor, are studied; and it is concluded that, for attached turbulent flows, the conventional s...

Extension of the Petrov-Galerkin Time-Domain Algorithm for Dispersive Media

The extension of an implicit, high-order, Petrov-Galerkin, time-domain, finite-element method for application to dispersive materials is derived and implemented. The resulting scheme does not require additional source terms to be added to Maxwells curl equations. While the emphasis of this research is the continued development of the Petrov-Galerkin algorithm for electromagnetic applications, the current formulation can also be used in a discontinuous-Galerkin scheme.

Computational optimization and sensitivity analysis of fuel reformer

Abstract In this study, the catalytic partial oxidation of methane is numerically investigated using an unstructured, implicit, fully coupled finite volume approach. The nonlinear system of equations is solved by Newton’s method. The catalytic partial oxidation of methane over rhodium catalyst in a coated honeycomb reactor is studied three-dimensionally, and eight gas-phase species (CH 4 , CO 2 , H 2 O, N 2 , O 2 , CO, OH and H 2 ) are considered for the simulation. Surface chemistry is modeled by detailed reaction mechanism including 38 heterogeneous reactions with 20 surface-adsorbed species for the Rh catalyst. The numerical results are compared with experimental data and good agreement is observed. Effects of the design variables, which include the inlet velocity, methane/oxygen ratio, catalytic wall temperature, and catalyst loading on the cost functions representing methane conversion and hydrogen production, are numerically investigated. The sensitivity analysis for the reactor is performed using three different approaches: finite difference, direct differentiation and an adjoint method. Two gradient-based design optimization algorithms are utilized to improve the reactor performance.