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Derivation and application of a class of generalized impedance boundary conditions, part 2
Boundary conditions involving higher order derivatives are presented by simulating surfaces whose reflection coefficients are known analytically, numerically, or experimentally. Procedures for determining the coefficients of the derivatives are discussed, along with the effect of displacing the surface where the boundary conditions are applied. Provided the coefficients satisfy a duality relation, equivalent forms of the boundary conditions involving tangential field components are deduced, and these provide the natural extension to non-planar surfaces. As an illustration, the simulation of metal-backed uniform and three-layer dielectric coatings is given. It is shown that fourth order conditions are capable of providing an accurate simulation for the uniform coating at least a quarter of a wavelength in thickness. Provided, though, some compromise in accuracy is acceptable, it is also shown that a third order condition may be sufficient for practical purposes when simulating uniform coatings.
Quantification of Dynamic Differences Between Boundary Conditions for Environment Specification Improvement.
Abstract not provided.
A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions
Not Available
Impact of Lateral Groundwater Flow and Subsurface Lower Boundary Conditions on Atmospheric Boundary Layer Development over Complex Terrain
Credible soil moisture redistribution schemes are essential to meteorological models, as lower boundary moisture influences the balance of surface turbulent fluxes and atmospheric boundary layer (ABL) development. While land surface models (LSMs) have vastly improved in their hydrologic representation, several commonly held assumptions, such as free-draining lower boundary, one-dimensional moisture flux, and lack of groundwater representation, can bias the terrestrial water balance. This study explores the impact of LSM hydrology representation on ABL development in the Weather Research and Forecasting (WRF) meteorological model. The results of summertime WRF simulations with Noah LSM, characterized by 2-m-thick soil and one-dimensional flow, are shown for a domain in the Colorado Rocky Mountain headwaters region. A reference WRF simulation is compared to 1) the same model with soil moisture initialized by the hydrologic model ParFlow; 2) a deep, free-draining simulation; and 3) WRF coupled to ParFlow, a three-dimensional, integrated groundwater-surface water model. Results show that both lateral transport of groundwater and the rate of drainage from the lower soil layer can weaken or reverse the coupling strength between evaporative fraction and ABL over a 5-month summer period. The resulting shifts in low-level moist convection in river valleys and thermally driven airflows yield strengthened anabatic upslope winds and perturbations to regional precipitation.
Inflow/Outflow Boundary Conditions with Application to FUN3D
Several boundary conditions that allow subsonic and supersonic flow into and out of the computational domain are discussed. These boundary conditions are demonstrated in the FUN3D computational fluid dynamics (CFD) code which solves the three-dimensional Navier-Stokes equations on unstructured computational meshes. The boundary conditions are enforced through determination of the flux contribution at the boundary to the solution residual. The boundary conditions are implemented in an implicit form where the Jacobian contribution of the boundary condition is included and is exact. All of the flows are governed by the calorically perfect gas thermodynamic equations. Three problems are used to assess these boundary conditions. Solution residual convergence to machine zero precision occurred for all cases. The converged solution boundary state is compared with the requested boundary state for several levels of mesh densities. The boundary values converged to the requested boundary condition with approximately second-order accuracy for all of the cases.
Formulation and Implementation of Inflow/Outflow Boundary Conditions to Simulate Propulsive Effects
Boundary conditions appropriate for simulating flow entering or exiting the computational domain to mimic propulsion effects have been implemented in an adaptive Cartesian simulation package. A robust iterative algorithm to control mass flow rate through an outflow boundary surface is presented, along with a formulation to explicitly specify mass flow rate through an inflow boundary surface. The boundary conditions have been applied within a mesh adaptation framework based on the method of adjoint-weighted residuals. This allows for proper adaptive mesh refinement when modeling propulsion systems. The new boundary conditions are demonstrated on several notional propulsion systems operating in flow regimes ranging from low subsonic to hypersonic. The examples show that the prescribed boundary state is more properly imposed as the mesh is refined. The mass-flowrate steering algorithm is shown to be an efficient approach in each example. To demonstrate the boundary conditions on a realistic complex aircraft geometry, two of the new boundary conditions are also applied to a modern low-boom supersonic demonstrator design with multiple flow inlets and outlets.
(U) Boundary Conditions for Ejecta Source Models with Stationary Velocity Distributions
We show that certain apparently universal features of the piezoelectric voltage traces measured in HE-driven tin coupon experiments [1, 2] constrain the functional form of any ejecta source model with a stationary velocity distribution. Building on an analytic formalism that has been extensively documented elsewhere [3, 4, 5, 6, 7], we derive simple expressions for V(t 0 a ), V'(t 0 a ), and the discontinuity in V(t break ) where t 0 a is the time of first ejecta arrival at the sensor and t break is the “depletion” time for the fastest particles arriving at the sensor. These three quantities appear to be zero, or nearly so, in the Vo- gan voltage data [1] (modulo noise and any smoothing effects created by the circuit); however, the predicted voltages for this general class of source models do not automatically achieve these conditions unless special boundary conditions are met. Source models which violate these boundary conditions will produce voltage predictions at odds with the measurements. The RMI+SSVD ejecta source model in its current formulation satisfies none of these boundary conditions, and therefore predictions from a stationary-velocity-distribution approximation to the RMI+SSVD source model deviate significantly from the voltage data. This analysis suggests straightforward methods for potentially improving the predictions of the RMI+SSVD ejecta source model. We test this with a simple adjustment to the SSVD and find, as anticipated, the adjustment corrects three properties of the voltage prediction. Furthermore, the adjusted model’s prediction for ejecta mass accumulation at the sensor exhibits a smoother and more gradual rise from the baseline than that produced by the original source model, thereby improving overall model/data agreement.
Magnetohydrodynamic boundary conditions for global models
Boundary conditions in the ionosphere and the upstream solar wind are important in determining the dynamics of global magnetohydrodynamic models of the magnetosphere. It is generally recognized that the orientation of the magnetic field in the upstream solar wind strongly modulates the rate of energy input into the magnetosphere by magnetic reconnection. However, other aspects of the upstream boundary conditions may determine whether the reconnection occurs in a patchy manner, as in flux transfer events, or in a global manner, as in the Paschmann et al. (1979) events. Ionospheric boundary conditions should also affect the reconnection process. For example, ionospheric line-tying can cause x-line motion in the outer magnetosphere. If it is assumed that auroras occur on field lines mapping to x-lines, then auroral motions are different than the local convective motion of the plasma in which they occur. Global magnetohydrodynamic models which incorporate both magnetospheric reconnection and ionospheric convection could be used to investigate the effect of reconnection and convection upon dayside and nightside auroral motions during the course of a magnetic substorm.
Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct Acoustics
Periodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.
A non-local computational boundary condition for duct acoustics
A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.
Validity condition for the local sheath impedance boundary condition and a nonlocal generalization
ICRF sheaths can cause unwanted interactions of high-power RF waves with material surfaces in magnetic fusion devices. In previous work, a local RF sheath impedance boundary condition (BC) was derived for use in ICRF codes together with a microscale (i.e., Debye or sheath width scale) model for obtaining the sheath impedance used in that BC. This local RF sheath BC matches the normal component of current and electrostatic potential across the sheath-plasma interface. Collapsing the matching conditions at the sheath-plasma interface to a BC depends on the assumption of scale separation, which can be violated when conditions along the local radius of curvature of the surface vary sufficiently rapidly. The validity condition is explored in this contribution, with special attention to the case where the magnetic field approaches being tangent to the surface. When the local sheath BC no longer applies, a non-local sheath BC is developed under the assumption of a more relaxed scale separation assumption. It is shown that the non-local sheath BC reduces to the previous local sheath BC under appropriate conditions. Furthermore, a surface-integrated sheath admittance parameter describes the 2D physics in the new BC.
Boundary value problems with interior point boundary conditions
Self adjoint boundary value problems with interior point boundary conditions using differential operator in Hilbert space
Trajectory optimization techniques in chemical reaction engineering. I - Boundary condition iteration methods
Boundary condition iteration methods in chemical process plant optimal design and control, considering simplicity and ease of programming, computation time and storage requirements
How good is the impedance boundary condition?
The impedance boundary condition (IBC) is often used in scattering problems involving material-coated conducting bodies. It is shown that for some commonly encountered coating configurations, the value of the impedance varies significantly as functions of the incident angle and polarization. Hence, the use of IBC in a rigorously formulated problem may affect the accuracy of the final solution.
Large Eddy Simulation in a Channel with Exit Boundary Conditions
The influence of the exit boundary conditions (vanishing first derivative of the velocity components and constant pressure) on the large eddy simulation of the fully developed turbulent channel flow has been investigated for equidistant and stretched grids at the channel exit. Results show that the chosen exit boundary conditions introduce some small disturbance which is mostly damped by the grid stretching. The difference between the fully developed turbulent channel flow obtained with LES with periodicity condition and the inlet and exit and the LES with fully developed flow at the inlet and the exit boundary condition is less than 10% for equidistant grids and less than 5% for the case grid stretching. The chosen boundary condition is of interest because it may be used in complex flows with backflow at exit.
On the Implementation and Further Validation of a Time Domain Boundary Element Method Broadband Impedance Boundary Condition
A time domain boundary integral equation with Burton-Miller reformulation is presented for acoustic scattering by surfaces with liners in a uniform mean flow. The Ingard-Myers impedance boundary condition is implemented using a broadband multipole impedance model and converted into time domain differential equations to augment the boundary integral equation. The coupled integral-differential equations are solved numerically by a March-On-in-Time (MOT) scheme. While the Ingard-Myers condition is known to support Kelvin-Helmholtz instability due to its use of a vortex sheet interface between the flow and the liner surface, it is found that by neglecting a second derivative term in the current time domain impedance boundary condition formulation, the instability an be effectively suppressed in computation. The proposed formulation and implementation are validated using a NASA Langley Research Center Grazing Flow Impedance Tube (GFIT) experimental dataset with satisfactory results. Moreover, a minimization procedure for finding the poles and coefficients of the broadband multiple impedance model is formulated in this paper by which, unlike the commonly used vector-fitting method, passivity of the model is ensured. Numerical tests show the proposed minimization approach is effective for modeling liners that are commonly used in aeroacoustic applications.
Improved Boundary Conditions for Cell-centered Difference Schemes
Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.