Integral Equation-Based Nonoverlapping DDM Using the Explicit Boundary Condition

Within the context of a pressure-based finite volume method for simulating incompressible flow involving open boundaries, asolution procedure without the need for explicit boundary conditions at any open boundary is proposed. The sole information required in solving the discretized momentum and pressure-linked equations is the flow rate allocated to each of the open boundaries within the solution domain. The methodology isdemonstrated by simulating the laminar flow of an incompressible Newtonian fluid in a duct with a 90 degree branch.

A large number of studies, based on 3-axis end milling of free-form surfaces, seek to optimize tool path planning. Approaches try to optimize the machining time by reducing the total tool path length while respecting the criterion of the maximum scallop height. Theoretically, the tool path trajectories that remove the most material follow the directions in which the machined width is the largest. The free-form surface is often considered as a single machining area. Therefore, the optimization on the entire surface is limited. Indeed, it is difficult to define tool trajectories with optimal feed directions which generate largest machined widths. Another limiting point of previous approaches for effectively reduce machining time is the inadequate choice of the tool. Researchers use generally a spherical tool on the entire surface. However, the gains proposed by these different methods developed with these tools lead to relatively small time savings. Therefore, this study proposes a new method, using toroidal milling tools, for generating toolpaths in different regions on the machining surface. The surface is divided into several regions based on machining intervals. These intervals ensure that the effective radius of the tool, at each cutter-contact points on the surface, is always greater than the radius of the tool in an optimized feed direction. A parallel plane strategy is then used on the sub-surfaces with an optimal specific feed direction for each sub-surface. This method allows one to mill the entire surface with efficiency greater than with the use of a spherical tool. The proposed method is calculated and modeled using Maple software to find optimal regions and feed directions in each region. This new method is tested on a free-form surface. A comparison is made with a spherical cutter to show the significant gains obtained with a toroidal milling cutter. Comparisons with CAM software and experimental validations are also done. The results show the efficiency of the method.

A derivation of ordinary QED perturbation theory is given in the Schrödinger picture. The path integral is restricted to fields in a finite time interval, ti ≤ t ≤ tf, with explicit boundary conditions given by vacuum state functionals at the initial and final times. The free photon vacuum functional is uniquely specified by the requirement of stationarity in time. For the free electron vacuum further conditions need to be imposed, e.g., the occupation of all negative energy states. The calculations are carried out using a discretized time interval of finite spacing dt, and exact results (to all orders in dt) are obtained for the free generating functionals in Coulomb gauge. Hence Feynman diagrams may be evaluated before the limits of continuous and infinite time are taken, with 1/dt and 1/(tf − ti) providing, respectively, an ultraviolet and an infrared cut-off on the energy integrals. The method may also be used for studying the time evolution of interacting states, in particular of bound states.

Calculating the unknown coupled multiphysics fields from the known boundary condition is of great significance in computational physics. Existing classical algorithms are usually time consuming and resource demanding. Explosive growth in deep learning (DL) has provided a substitutive way to accelerate the calculation process by fully making use of the parallel computing capability of the graphics processing unit. In this work, a cascaded DL framework is presented to compute the coupled multiphysics fields related to electrical potential, temperature, velocity, etc. The whole framework is comprised of an input module and several Fourier modules, which achieves to acquire the coupled fields from the explicit boundary conditions. Compared with conventional networks, the Fourier network emerges consistent average error among different resolutions which saves training costs. As a result, a fully trained network can obtain the expected physics fields in real time, offering rosy prospects for practical scenarios.

On the extension problem for accretive differential operators

<p style='text-indent:20px;'>In this paper, the chaotic oscillations of the initial-boundary value problem of linear hyperbolic partial differential equation (PDE) with variable coefficients are investigated, where both ends of boundary conditions are nonlinear implicit boundary conditions (IBCs). It separately considers that IBCs can be expressed by general nonlinear boundary conditions (NBCs) and cannot be expressed by explicit boundary conditions (EBCs). Finally, numerical examples verify the effectiveness of theoretical prediction.</p>

The incidence of the numerical resolution and the blockage effect are investigated in an embedding method for solving bidimensional bluff body flows. This method consists of using an artificial boundary instead of imposing exact conditions on the body surface. It requires us to define a blur frontier ratio and a blockage effect ratio. The blockage effect ratio is found using the mean flow of a circular cylinder directly. The blur frontier ratio is obtained by comparison of the present method with another numerical method where explicit boundary conditions on the body are imposed. For this ratio, the investigations are based on the flow past a square cylinder which discard the uncertainty on the surface of the body for the embedding method. Hence, the two factors allow the transformations of the Strouhal and the Reynolds numbers for the flow past a circular cylinder. The universal Strouhal-Reynolds number relationship of the circular cylinder is finally recovered.

This paper extends the generating function approach to the state constrained linear quadratic optimal control problem by utilizing penalties. The original constrained problem is approximated by an unconstrained problem with a novel penalty function by which the latter problem can be solved via generating function method based on Taylor series approximation. In view of this, the optimal solution can be given as the state feedback control with explicit boundary conditions and pre-computed coefficients. This structure is useful in the repetitive on-line computation for optimal solutions satisfying a number of different boundary conditions. Examples demonstrate the effectiveness of the developed method.

Liquid metals are prospective coolant and working media for fission and fusion applications. In latter case they will be affected by very high magnetic fields. By now there is no possibility to recreate these conditions directly, and research is being made using numerical simulations and model liquids. Special care is taken to the possible thermogravitational phenomena in the presence of magnetic field. Temperature and temperature fluctuations are used to describe the flow structure as they can be obtained from experiments with high accuracy and localization. Area of intense fluctuations existence was explored using several experimental facilities including a new HELME Facility with magnetic fields of up to 2.7 Tesla. Area where fluctuations occur and specific of transition regions have been explored for the round vertical pipes with down flow and uniform heating (Grashof number of up to 1.2·108) as a basic configuration with explicit boundary conditions.

Numerical validation of the volume penalization method in three-dimensional pseudo-spectral simulations

We address in detail the numerical simulations of electromagnetic (EM) wave scattering from a mockup partly coated fighter jet in this presentation. The majority part of the fighter jet surface is considered to be perfect electric conductor (PEC). The horizontal stabilizer, vertical stabilizer and the wings are coated with high-density materials, whereas a hollow dielectric radome is located at the front of the aircraft. Due to the nature of unbounded problem domain, and the desire to avoid a three dimensional discretization, we attempt to compute the numerical approximation using the boundary integral equations (BIEs), or the method of moments (MoM). However, it turns out not to be an easy quest. In the presentation, we shall elucidate difficulties that we have encountered and innovative techniques that we have devised during our journey to solve such a challenging mutli-scale EM application.

The ring test has been devised to measure friction paratmeters under extreme pressure conditions as in metal forming processes. However, gravely erroneous assumptions are used to develop and interpret the test. The continuum difinition of stress is violated not only by the test theory but also by the current concepts of friction and lubrication. The author has proposed a general solution for the contact problem based primarily on the continuum definition of stress as a local quantity. An experimental procedure, following Bridgman’s shear-compression fracture tests is proposed to measure frictional properties in a new format. The resulting information is introduced in the analysis as explicit displacement or traction boundary conditions. The incremental nature of the nonlinear boundary value problem involving the deforming media in contact is conveniently used to generate a discretized approximation to the state of stress and deformation along the contact surface at the end of each solution increment. An important consequence of this approach is that the symmetry of the stiffness matrix in the finite element analysis is insured, resulting in considerable computational savings. Another advantage of the proposed method is the elimination of non-physical corner stress singularities. Moreover, recognition of the local nature of contact stresses implies that the proposed method is applicable to any geometry of contact.

Local explicit feedback boundary conditions are given for the stabilization in \(L^2-\)norm of the 2-D shallow water model. The proposed method is based on symmetrization of the flux matrices of the linearized model and analysis of the Riemann invariants. The non-conservative 2-D shallow water equations are linearized around the target steady state sub-critical flow. The established feedback control laws guarantee a decay of the energy of the perturbation model. We present numerical simulations to demonstrate how the proposed controller works for the linearized as well as nonlinear shallow water problem.

The electric field integral equation (EFIE) is one of simpl formulations of boundary integral equations for Maxwell's equations. It is widely known that the discretised EFIE is ill-conditioned, namely iteration methods to solve the discretised EFIE require a lot of iteration numbers, which results in much computational time. One of effective solutions to this problem is the Caldern preconditioning The Caldern preconditioning constructs a preconditioner based on the so-called Caldern formula, which implies that the square of the electric field integral operator (EFIO) is well-conditioned. Unfortunately simple discretisation of the squared EFIO is known to break down. Hence, in many previous studies of the Caldern preconditioning for the EFIE, the dual basis function is used in addition to the standard basis function, such as the Buffa-Christiansen (BC) basis function Although the Caldern preconditioning can be successfully implemented with the BC and RWG functions, discretisation of the EFIO with the BC basis function takes much more computational time than that with the RWG function. On the other hand our group has found that the dual basis function for the roof-top basis function defined on a quadrilateral mesh is also the roof-top basis function

For efficient EM space modeling, it is very often needed an optimal type of meshing. Techniques and algorithms for meshing in triangles are much developed than another mesh type. In this paper, we present a resolution of 2-D time domain electric field integral equation with RWG functions (Rao, Wilton and Glisson's function) using novel mesh technique based on hexagonal mesh. (TD-IE) are applied to analyze transient radiation from square plate illuminated by an incident electromagnetic wave. A new basis function derived from RWG functions is used as space base and Laguerre functions as temporal basis function. Numerical results that validate and demonstrate the efficacy and accuracy of the proposed technique are presented and compared with another mesh technique.