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Stalcup, Erik JamesNumerical Modeling of Upward Flame Spread and Burning of Wavy Thin Solids
Master of Sciences, Case Western Reserve University, EMC - Aerospace Engineering
Flame spread over solid fuels with simple geometries has been extensively studied in the past, but few have investigated the effects of complex fuel geometry. This study uses numerical modeling to analyze the flame spread and burning of wavy (corrugated) thin solids and the effect of varying the wave amplitude. Sensitivity to gas phase chemical kinetics is also analyzed. Fire Dynamics Simulator is utilized for modeling. The simulations are two-dimensional Direct Numerical Simulations including finite-rate combustion, first-order pyrolysis, and gray gas radiation. Changing the fuel structure configuration has a significant effect on all stages of flame spread. Corrugated samples exhibit flame shrinkage and break-up into flamelets, behavior not seen for flat samples. Increasing the corrugation amplitude increases the flame growth rate, decreases the burnout rate, and can suppress flamelet propagation after shrinkage. Faster kinetics result in slightly faster growth and more surviving flamelets. These results qualitatively agreement with experiments.

Committee:

James T'ien (Committee Chair); Joseph Prahl (Committee Member); Yasuhiro Kamotani (Committee Member)

Subjects:

Aerospace Engineering; Fluid Dynamics; Mechanical Engineering

Keywords:

modeling;simulation;numerical modeling;combustion;computational combustion;direct numerical simulation;flame spread;burning;wavy;corrugated;fire dynamics simulator;FDS;fuel structure;fuel geometry;complex geometry;cardboard;

Lee, Hwa OkNumerical Modeling of Electromagnetic Well-Logging Sensors
Doctor of Philosophy, The Ohio State University, 2010, Electrical and Computer Engineering

In this dissertation, we develop time-domain numerical algorithms to model the electromagnetic responses of logging-while-drilling (LWD) tools in complex Earth formations. The increasing need to model complex features of realistic formations calls for the development of increasingly sophisticated and flexible numerical algorithms. The new algorithms proposed in this dissertation are based upon the finite-difference time-domain (FDTD) framework. FDTD is highly suited for the purposes because it is matrix-free and discretizes Maxwell's equations directly on a discrete grid of points, providing unparalleled flexibility in handing complex Earth media.

In this dissertation, we employ FDTD directly in three-dimensional cylindrical coordinates, which suppress the staircasing error incurred when discretizing the cylindrical tool geometry, while keeping the method matrix-free. Another limitation of FDTD is its conditionally stability, which limits the maximum time increment that can be used on the marching-on-time algorithm. This maximum time increment is set up the Courant criterion and is proportional to the spatial cell size used. The Courant criteria leads to oversampling in time whenever a very fine spatial discretization is required. This implies excessive computation times. As an alternative to FDTD, the alternating direction implicit (ADI)-FDTD method offers unconditionally stability with little extra computation effort, which includes the need to solve a tridiagonal system at each time-step.

In order to properly truncate the computational domain in the modeling of open-space problems, an absorbing boundary condition is also needed. Here, a convolutional perfectly-matched-layer (CPML) absorbing boundary condition based on a complex frequency shifted (CFS) stretching and recursive convolution is developed and implemented in the 3-D cylindrical ADI-FDTD algorithm. Because the time step size in the ADI-FDTD simulations cannot be increased arbitrarily due to numerical errors such as splitting errors and numerical (grid) dispersion, a complex-envelope (CE) technique is further incorporated into the ADI-FDTD algorithm. The cylindrical CE-ADI-FDTD makes it possible to reduce the overall computation time while maintaining the dispersion error at reasonable levels.

In order to further reduce the computational time, this dissertation also develops a heterodyne approach for time-domain simulations in highly refined grids. The proposed approach is based on a complex-envelope algorithm with a carrier frequency and a complex-valued FDTD algorithm with a shifted spectrum centered at a higher simulation frequency. This corresponds to a shorter period and faster convergence for narrowband simulations. In practice, the logging tool axis is frequently misaligned with the borehole axis due to gravitational pull effects and/or mechanical vibrations. In addition, Earth media exhibits anisotropy which is represented by a full conductivity tensor during deviated drilling. The study of anisotropy and eccentricity is important for correct interpretation of logging data. A new locally-conformal (LC) FDTD based on deriving effective anisotropic tensor conductivities for partially-filled grid cells, composed of an isotropic conductive region representing the borehole and an anisotropic conductive region representing the Earth formation, is developed using a quasi-static approximation. The new LC-FDTD algorithm allows for employing coarser grids than conventional FDTD, and hence for obtaining faster simulation times, for a given required accuracy level.

Committee:

Fernando L. Teixeira, PhD (Advisor); Roberto G. Rojas, PhD (Committee Member); Joel T. Johnson, PhD (Committee Member)

Subjects:

Electromagnetism

Keywords:

numerical modeling; FDTD; well-logging

Safaei Jazi, RaminSimulation of Groundwater Flow System in Sand-Lick Watershed, Boone County, West Virginia (Numerical Modeling Approach)
MS, Kent State University, 2012, College of Arts and Sciences / Department of Geology
Determining the hydraulic properties of aquifer and aquitards (K,T,and S) is very important in hydrogeologic studies. These parameters can be identified by methods such as laboratory permeability and borehole hydraulic response test. Because these approaches are sometimes costly, involving drilling test holes, and often may not be feasible, numerical modeling approaches can be considered as alternatives. In the following study, numerical modeling is applied to simulate groundwater flow system to determine the hydraulic properties of a weathered/fractured zone in a valley located within the Appalachian Plateau Geomorphic Province. The Appalachian Plateau is characterized by relatively flat-laying but intensely eroded bedrock, comprising cyclical sequences of Pennsylvanian age sedimentary bedrock dominated by sandstone, siltstone, shale, coal, claystone, and occasionally limestone. Fractured/weathered sandstone is potentially the main bedrock groundwater transmitting formation. The extent of fractures is from the ground surface to about 120-150 ft (or roughly 30-40m) under the ground surface. The main groundwater flow occurs from within the intergranular pore space through fractures and along bedding planes of the bedrock. The water level at a perennial stream in the valley can be considered as the phreatic ground-water level. Therefore, the elevation points along this stream may serve as model calibration points. Because the outflow from the valley is almost entirely via the creek, and creek water represents the groundwater level all along the valley, the model is calibrated and verified by the creek water elevations and the amount of water discharging through the valley. The site- specific hydrogeologic interpretation and evaluation technique presented in this study may be very well applicable to the significant portions of the Allegheny Plateau with similar geomorphologic, tectonic and lithologic characteristics.

Committee:

Yoram Eckstein, Professor (Advisor)

Subjects:

Geology; Hydrologic Sciences

Keywords:

Hydraulic property; Aquifer; Numerical modeling; Appalachian Plateau

Ge, Yang3D numerical study on droplet-solid collisions in the Leidenfrost regime
Doctor of Philosophy, The Ohio State University, 2005, Chemical Engineering
A 3-dimensional numerical model is developed to simulate the process of collision between an evaporative droplet and a high-temperature solid object in this study. Such phenomena are of direct relevance to many engineering problems. The simulation model of this study is built upon advanced DNS (direct numerical simulation) techniques, coupled with a finite-volume algorithm in the fixed Eulerian grid. The 3D level-set method is employed to portray the droplet surface variation during its deformation. The immersed boundary method is applied to impose the solid-fluid boundary condition at the particle surface. To account for the micro-scale resistant effect induced by the film-boiling evaporation of the droplet, a vapor flow model is developed to calculate the pressure and velocity distributions along the vapor layer between the droplet and the solid. The temperature fields in all phases and the evaporation rate on the droplet surface are illustrated using a full-field heat transfer model. The comparisons of the simulation result with the experimental observation reveal the accuracy of the model, and the convergence is analyzed and verified by using different grid sizes in the computation. For saturated impact, the oscillation of the thickness of the vapor layer and the temperature at solid surface are calculated and compared favorably with the experimental results. The sub-cooled impact yields a thinner vapor layer and a higher heat transfer rate compared to the saturated impacts, and thus the kinetic discontinuity at the liquid-vapor and solid-vapor boundaries in the slip flow regime need to be considered. The effects of the droplet’s initial temperature are analyzed using the present model, and it shows that the droplet subcooling degree is significantly related to the thickness of the vapor layer and the heat flux at the solid surface. The collision process between an evaporative droplet and a high-temperature particle is investigated through numerical simulation and the experiment. The effects of the particle size and the collision velocity are examined numerically. Simulation model is further applied to study the oblique collision between the droplet and the particle. The effects of the obliquity on the outcome of the collision are analyzed.

Committee:

Liang-Shih Fan (Advisor)

Keywords:

Droplet; Collision; Simulation; Leidenfrost; Particle; Numerical modeling

Ramanathan, Arun Kumar KumarDynamic response of a shipping container rack and suspended automotive parts under random excitation: Experimental, Computational and Analytical Studies
Master of Science, The Ohio State University, 2017, Mechanical Engineering
Shipping containers are exposed to complex dynamic loading conditions during transport via truck, rail, and air. The loading conditions are further complicated by contact gap nonlinearities between the cart and ground, cart holders and suspended parts, and between neighboring suspended parts. This study focuses on developing a modeling strategy to simulate a container cart with parts undergoing random vibration tests based on standard road profiles. Initially, the linear system response to a random excitation profile of the cart structure is examined in frequency domain and correlated with experimental measurements. The linear system predictions lacked the required modeling fidelity to capture the nonlinear dynamic behavior observed during the testing as the container is loaded. Thus, the nonlinear response is then simulated in time domain using the explicit integration method with contact-driven boundary conditions using a commercially available finite element software. The total run time is determined to be prohibitively long for the time domain formulation, say over 5 seconds with a time step size of 0.3 microsec. Finally, a dynamic substructuring strategy is employed and implemented using super elements in the commercial finite element code. This particular method captured the dynamic amplification of the cart, maintained the contact nonlinearities, and reduced the computational burden. Further, a minimal order lumped model of the dynamic system is developed to understand the physics of the problem. Both lumped and finite element models consistently captured the nonlinear random vibration phenomenon and predicted the overall acceleration levels within 20% of measurements.

Committee:

Rajendra Singh (Advisor); Jason Dreyer (Committee Member); Scott Noll (Committee Member)

Subjects:

Engineering; Mechanical Engineering; Packaging

Keywords:

packaging, transport vibrations, dynamic substructuring, finite element analysis FEA, nonlinear lumped models, numerical modeling, random vibration tests

ZHANG, JIEHAINUMERICAL SIMULATIONS OF STEADY LOW-REYNOLDS-NUMBER FLOWS AND ENHANCED HEAT TRANSFER IN WAVY PLATE-FIN PASSAGES
PhD, University of Cincinnati, 2005, Engineering : Mechanical Engineering
Extended or finned surfaces are widely used in compact heat exchangers to reduce the thermal resistance of air- or gas-side flows. Besides increasing the effective heat transfer surface area, geometrically modified finned surfaces also improve the heat transfer coefficient by altering the flow field. Wavy plate-fin surfaces have such properties and promote relatively high thermal-hydraulic performance. They are also attractive for their simplicity of manufacture and ease of use in compact heat exchangers. The current study numerically investigates the fluid flow and enhanced convection heat transfer in two-dimensional and three-dimensional wavy plate-fin passages with sinusoidal wall corrugations in the low Reynolds number regime. Constant property, periodically fully developed, and laminar or low Reynolds number forced convection are considered. The governing equations of continuity, momentum, and energy are solved computationally using finite-volume techniques. The solution procedure is based on the SIMPLE algorithm and a non-orthogonal, non-uniform grid. The influences of fin geometry (fin spacing, fin height, fin amplitude and fin length) on the enhanced heat transfer and fluid flow behaviors are investigated. The simulation results for the velocity and temperature distributions, isothermal Fanning friction f, and Colburn factor j are presented and discussed. The complex flow patterns in the wavy-fin channel are characterized by re-circulating and/or helical swirl flows with periodic flow separation and reattachment. Two flow regimes can be classified based on these results, namely, (1) low-Re streamline-flow regime where viscous forces dominate, and (2) high-Re swirl-flow regime characterized by flow recirculation and/or helical vortices. Heat transfer enhancement is observed in the swirl flow regime along with an increased pressure drop penalty, as a consequence of the periodic thermal boundary-layer thinning, strong flow mixing, and periodic generation and dissipation of vortices or re-circulating cells. In the streamline-flow regime, the flow and heat transfer behavior are similar to that in straight flow channel, though an enhanced performance is obtained. Also, results of flow visualization experiment for a two-dimensional wavy flow channel are shown to agree well with the numerical results. Finally, the computational methodology is extended to illustrate the flow behaviors in out-of-phase wavy flow passages.

Committee:

Dr. Raj Manglik (Advisor)

Subjects:

Engineering, Mechanical

Keywords:

Wavy plate-fin; enhanced heat transfer; numerical modeling and simulation

Young, Nathan LeeEffect of Rivers on Groundwater Temperature in Heterogeneous Buried-Valley Aquifers: Extent, Attenuation, and Phase Lag of Seasonal Variation
Master of Science (MS), Wright State University, 2014, Earth and Environmental Sciences
The temperature of groundwater in aquifers is relatively stable when compared to the water temperature in surface-water bodies. However, in aquifers that are hydraulically connected to rivers that have water flux into the aquifer, the local aquifer temperature can show seasonal variation. This project focused on the thermally-altered, near-river zone of such an aquifer, and used numerical methods to examine the extent of seasonal variation in temperature into the aquifer, and the attenuation and phase shift of the signal with distance from the river. The results show that the extent of alteration by diffusive heat flow is negligible compared to the advective component of heat flow. Therefore, because heat transport is driven primarily by advection, the extent of seasonal variation in temperature into the aquifer, as well as the attenuation and phase lag of the signal are significantly dependent on the hydraulic gradient between the river and aquifer. Furthermore, the extent, attenuation, and phase lag of seasonal variation in temperature within the aquifer was found to be strongly dependent on heterogeneity. Considerable differences in the expression of the seasonally varying temperature signal were found to occur as a result of the local presence of high and/or low hydraulic conductivity material. Finally, for the Miami Valley aquifer (which the models used in this study were based upon), seasonal variation in groundwater temperature is expected only within a lateral distance of about 135 meters from the river and there only within a depth of about 25 meters.

Committee:

Robert Ritzi, Ph.D. (Advisor); David Dominic, Ph.D. (Committee Member); Chris Barton, Ph.D. (Committee Member)

Subjects:

Environmental Geology; Environmental Science; Geology

Keywords:

Hydrogeology, ground water temperature, seasonal variation of river temperature, open-loop geothermal, numerical modeling, buried-valley aquifers, aquaculture, losing streams, river-aquifer gradients

Kini, Satish D.An approach to integrating numerical and response surface models for robust design of production systems
Doctor of Philosophy, The Ohio State University, 2004, Industrial and Systems Engineering

Before production, experience and deterministic simulations are used to design the dies for the chosen part. Experience is mainly used for process design and input parameter selection. During production few parts are manually inspected to see if they are within specifications and have no defects. Control charts are also used by operators to make process changes based on experience if parts are out of tolerance.

Conventionally, deterministic finite element methods (FEM) are used for die design in production systems and experience is mainly used for process design. However in reality, process conditions vary with time and hence with the same nominal process settings it is likely that the final forged part geometry varies with time. The simulations will give us solutions which may not match with the actual part geometries.

In order to solve this problem, an approach to integrating numerical and response surface models for robust process design is described in this research. The integrated model is a virtual production model (VPM) which integrates numerical modeling techniques with response surface methodology (RSM). The VPM is driven by a combination of FEM, RSM and stochastic simulations. The production system is modeled as a series of processes with input parameters having distributions and output attributes which vary with time. The tasks to develop the model include deterministic FEM simulations, development of response surfaces of attributes and stochastic simulations. This model will be used to design the existing production process by designing the best input parameter settings. Its main aim is reducing process variability, reducing defect rates and improving process capability by robust process design.

In this dissertation two approaches for integrating numerical models and response surface models have been described. The first approach integrates well established empirical relations, Taguchi methods of experimental design and FEM to arrive at robust roll pass designs. The second approach integrates FEM, RSM and stochastic simulations to develop a model of the production system. This model is then used for robustness analysis and improvement of the existing production system.

Committee:

Rajiv Shivpuri (Advisor)

Keywords:

Numerical modeling; Finite element method; Response surface methodology; Stochastic simulations; Monte Carlo method; Robust design; Production systems

Endo, MakotoNumerical modeling of flame spread over spherical solid fuel under low speed flow in microgravity: Model development and comparison to space flight experiments
Doctor of Philosophy, Case Western Reserve University, 2016, EMC - Mechanical Engineering
Flame spread over solid fuel presents distinctive characteristics in reduced gravity, especially when the forced flow velocity is low. The lack of buoyancy allows a blue, dim flame to sustain where the induced velocity would otherwise blow it off. At such low velocities, a quenching limit exists where the soot content is low and the effect of radiative heat loss becomes important. The objective of this study is to establish a high fidelity numerical model to simulate the growth and extinction of flame on solid fuels in a reduced gravity environment. The great importance of the spectral dependency of the gas phase absorption and emission were discovered through the model development and therefore, Statistical Narrow-Band Correlated-k (SNB-CK) spectral model was implemented. The model is applied to an experimental con figuration from the recent space experiment, Burning And Suppression of Solids (BASS) project conducted aboard the International Space Station. A poly(methyl methacrylate) (PMMA) sphere (initial diameter of 2cm) was placed in a small wind tunnel (7.6cm x 7.6cm x 17cm) within the Microgravity Science Glovebox where flow speed and oxygen concentration were varied. Data analysis of the BASS experiment is also an important aspect of this research, especially because this is the first space experiment that used thermally thick spherical samples. In addition to the parameters influencing the flammability of thin solids, the degree of interior heat-up becomes an important parameter for thick solids. For spherical samples, not only is the degree of internal heating constantly changing, but also the existence of stagnation point, shoulder, and wake regions resulting in a different local flow pattern, hence a different flame-solid interaction. Parametric studies using the numerical model were performed against (1) chemical reaction parameters, (2) forced flow velocity, (3) oxygen concentration and (4) amount of preheating (bulk temperature of the solid fuel). Flame Spread Rate (FSR) was used to evaluate the transient effect and maximum flame temperature, standoff distance and radiative loss ratio were used to evaluate the spontaneous response of the gas phase to understand the overall response of the burning solid fuel. After evaluating the individual effect of each parameter, the efficacy of each parameter was compared. Selected results of this research are: [1] Experimental data from BASS and numerical simulation both showed that within the time period between ignition until the flame tip reaches the shoulder of the sample, the flame length and time have almost a linear relation. [2] Decreasing forced flow velocity increases the radiative loss ratio whereas decreasing oxygen mole fraction decreases the radiative loss ratio. This fi nding must be considered in the effort to replicate the behavior of flame spread over thick solid fuels in microgravity on earth. [3] Although the standoff distance will increase when the forced flow velocity is decreased as well as when the oxygen mole fraction is decreased, the forced flow velocity has a much stronger effect on the standoff distance than the oxygen mole fraction. [4] Unlike the previous two comparisons, the effect of forced flow velocity and oxygen mole fraction on the maximum flame temperature was at similar level, reduction of either parameter would result in lowering the maximum flame temperature. [5] The effect of preheating on the flame spread rate becomes stronger when either the oxygen flow rate or forced flow velocity becomes larger. Depending on which element is more important, we can distinguish oxygen flow rate driven flame spread from preheating driven flame spread. Findings of this research are being utilized in the design of the upcoming space experiment, Growth and Extinction Limits of solid fuel (GEL) project. This research is supported by the National Aeronautics and Space Administration (NASA). This work made use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University and the Ohio Supercomputer Center.

Committee:

James S. T'ien (Committee Chair); Yasuhiro Kamotani (Committee Member); Fumiaki Takahashi (Committee Member); Erkki Somersalo (Committee Member)

Subjects:

Aerospace Engineering; Mechanical Engineering

Keywords:

Numerical modeling; flame spread; solid fuel; spherical fuel; microgravity; combustion; space experiment; NASA; GEL; SoFIE; SNB-CK; Radiation; Heat transfer; Finite Element; FEM; FDS; Microgravity Experiment; NASA-STD-6001; BASS; SIFI; FSR; axisymmetric;

Hernandez, Jaime A.Evaluation of the Response of Perpetual Pavement at Accelerated Pavement Loading Facility: Finite Element Analysis and Experimental Investigation
Master of Science (MS), Ohio University, 2010, Civil Engineering (Engineering and Technology)
This thesis presents the results of the experimental testing program performed at the Accelerated Pavement Load Facility (APLF) of Ohio University on four pavement test sections. The influence of load, temperature, offset, and thickness on the pulse duration and strain at the bottom of the asphalt concrete layer is discussed. A three-dimensional finite element model is developed in Abaqus. This numerical model prediction was compared to the results brought by the response model of the Mechanistic-Empirical Pavement Design Guide (MEPDG). The results of the experimental testing showed that the applied load does not affect the longitudinal pulse duration and that the influence of the offset depends on the magnitude of the applied load. Furthermore, the influence of the temperature on the mentioned variable is more significant at a high value (104°F) when it is compared to intermediate (70°F) or low values (40°F). In regards to the thickness, it was seen that the peak longitudinal tensile strain decrease at a higher rate when it passes 14.0 in.; this behavior is more evident at high values of temperature. In addition, it was found that the finite element model captured both: the pulse duration and the longitudinal strain at any value of load and temperature. The MEPDG procedure was able to predict the tensile strain at low and intermediate temperature, but it did not capture the longitudinal pulse duration in any case. In addition, the MEDPG procedure underestimates the peak longitudinal tensile strain under high values of applied load. Finally, it was concluded that the pavement response at the bottom of the asphalt concrete layer and at the top of the subgrade are not greatly influenced by the tire-pavement contact stress distribution assumption. However, it was found that in order for the finite element model to capture the effect of the offset, a stress distribution that takes into account the treads of the tire and the nonuniform stress distribution should be used.

Committee:

Shad Sargand, PhD (Advisor)

Subjects:

Civil Engineering; Experiments; Mechanics

Keywords:

MEPDG; Fatigue Cracking; Numerical Modeling; Abaqus; Accelerated Pavement Loading Facility; Tensile Strain; Pulse Duration

Cajko, FrantisekNano-Focusing of Light: Electromagnetic Analysis and Simulation
Doctor of Philosophy, University of Akron, 2009, Electrical Engineering

Over the last decades, there has been an ever increasing interest in nano-focusing oflight and subwavelength resolution overcoming the classical diffraction limit. Examples of that are scanning near-field optical microscopy (SNOM) and “perfect lenses” with negative-index materials. Development of scanning techniques, better performing probes for SNOM and engineering of effective material parameters depends on numerical modeling more than ever before. More accurate models and precise simulations are required to obtain quantitative rather than just qualitative results.

This dissertation discusses numerical challenges of nano-scale structure simulations with enhanced and strongly localized electric field distributions. In particular, the thesis focuses on the simulation of scattering-type apertureless SNOM in the mid-infrared and field distributions in plasmon-enhanced Raman spectroscopy in the visible range. Although the ideas of field enhancement are similar (sharp, optionally plasmon-coated, object causing a strong localized enhancement in the vicinity of an AFM tip), applicable models and the nature of computational and engineering challenges are different.

For the plasmon-enhanced SNOM, the quasi-static and the full-wave FEM analyses are compared and a qualitative agreement is shown. The optical response of the AFM tip is shown to correlate with the amplitude of the local field distribution. This allows one to use dark field microscopy for tip testing. Several tip designs proposed in the literature were analyzed using the quasi-static approximation; parametric analysis and optimization were performed for selected tips.

Numerical challenges due to the multi-scale nature of the problem and multiple scattering in scattering-type SNOM are exemplified in 3D simulations of a realistic cantilevered AFM tip in the mid-infrared. The finite element method (FEM) with adaptive meshing is shown to be a useful tool, but the computation resources of a standard PC must be stretched to their limits. Near and far fields were analyzed and an excellent agreement of the direct back-scattered field with experimental results observed.

A substantial part of the dissertation deals with FLAME  ” a generalized FD calculus. Numerical problems related to high-precision calculation of the coefficients of the scheme for fine grids are pointed out and overcome. A spurious space of solutions in the case of multiple possible schemes is discovered and remedies proposed. Numerical problems of FD for materials with a negative index of refraction are pointed out and the performance of FLAME is investigated.

Advantages of FLAME over standard schemes for interfaces with negative index materials (NIM) are demonstrated on an example of a NIM slab in air.

Committee:

Igor Tsukerman, PhD (Advisor)

Subjects:

Electrical Engineering; Electromagnetism; Optics

Keywords:

electromagnetic analysis; electrostatics; wave analysis; numerical modeling; negative refraction; NIM; apertureless SNOM; TERS; finite elements; FEM; flexible local approximation; FLAME