Boundary Discretization Method Research Articles

An Improved Subdomain Model for Predicting the Magnetic Field of a Motor Containing Non-Orthogonal Boundaries

In this paper, the boundary discretization method is used to improve the traditional subdomain model. The improved model can be used to calculate the magnetic field distribution in the region containing non-orthogonal boundary, avoiding the influence of the simplified stator slot or permanent magnet shape on the results in calculating the motor magnetic field using the traditional subdomain model. In addition, the improved subdomain model can also be used to calculate the air-gap flux density when the rotor is eccentric, instead of segmenting the air-gap to an equivalent state without eccentricity. The calculation object of this paper is a surface-mount permanent magnet motor with a rectangular stator slot. The air-gap flux density under no-load and load conditions is calculated, respectively. Since the improved subdomain model does not need to simplify the stator slot shape, the magnetic potential in the stator slot is also calculated. Finally, the air-gap flux density under rotor eccentricity is calculated, and the influence of the calculating parameters on the results of the improved subdomain model is discussed. All the calculated results are compared with those obtained by the finite element method, which verifies the accuracy of the improved calculation model.

Highly efficient computation method for hazard quantification of uncontained rotor failure

Uncontained Engine Rotor Failure (UERF) can cause a catastrophic failure of an aircraft, and the quantitative assessment of the hazards related to UERF is a very important part of safety analysis. However, the procedure for hazard quantification of UERF recommended by the Federal Aviation Administration in advisory circular AC20-128A is cumbersome, as it involves building auxiliary lines and curve projections. To improve the efficiency and general applicability of the risk angle calculation, a boundary discretization method is developed that involves discretizing the geometry of the target part/structure into node points and calculating the risk angles numerically by iterating a particular algorithm over each node point. The improved efficiency and excellent accuracy for the developed algorithm was validated through a comparison with manual solutions for the hazard quantification of the engine nacelle structures of a passenger aircraft using the guidance in AC20-128A. To further demonstrate the applicability of the boundary discretization method, the proposed algorithm was used to examine the influence of the target size and the distance between the target and rotor on the hazard probability.

Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters

The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber’s hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.

Estimation of the local convective heat transfer coefficient in pipe flow using a 2D thermal Quadrupole model and Truncated Singular Value Decomposition

The techniques for solving the Inverse Heat Conduction Problem represent useful tools for designing heat transfer apparatuses. One of their most challenging applications derives from the necessity of catching what happens inside a heat transfer apparatus by monitoring the temperature distribution on the external wall of the device, possibly by means of contactless experimental methodologies. The research presented here deals with the application of a solution strategy of the Inverse Heat Conduction Problem (IHCP) aimed at estimating the local heat transfer coefficient on the internal wall surface of a pipe, under a forced convection problem. The solution strategy, formulated for a 2D model, is based on the Quadrupole Method (QM) coupled to the Truncated Singular Value Decomposition approach, used to cope with the ill-conditioning of the problem. QM presents some advantages over the more classical domain or boundary discretization methods as for instance the fact that, being meshless, brings to a reduction of the computational cost. The analytical model, built under the QM, is validated by means of numerical simulations and the numerical outputs are then used as synthetic data inputs to solve the IHCP. The estimation methodology is also applied to experimental data regarding a forced convection problem in coiled pipes. Moreover, the adopted solution technique is compared to other two well-known and consolidated approaches: Finite Element Method coupled to the Tikhonov Regularization Method and Gaussian Filtering Technique. The comparison highlights that, for the problem here investigated, the Quadrupole Method coupled to the Truncated Singular Value Decomposition and Finite Element Method coupled to the Tikhonov Regularization Method perform better than the Gaussian Filtering Technique when the noise level is low, while, for higher noise level values, their efficiency is almost comparable, as it happens in the considered experimental study case.

A mesh-less method to solve electrical resistance tomography forward problem using singular boundary distributed source method

This paper presents a novel mesh-less method called singular boundary distributed source (SBDS) method to solve the electrical resistance tomography (ERT) forward problem. Mesh-less methods are mathematically simple and computationally efficient i.e. same accuracy that of mesh or domain based methods can be achieved with less computation time. The domain boundary is discretized such that the source and field points coincide on the same boundary and the solution is expressed as a linear combination of fundamental solution of governing equation. The singularity appearing due to coinciding of source and field points is addressed using a hybrid approach. The coefficients corresponding to Neumann boundary are evaluated using the improved distributed source method (IBDS) while the coefficients corresponding to Dirichlet boundary conditions are evaluated using inverse interpolation technique. The hybrid SBDS with complete electrode model is formulated for ERT forward problem. The proposed SBDS method has better accuracy and convergence as compared to other mesh-less methods. Especially, the SBDS method solution is not dependent on distributed source radius therefore is stable compared to the IBDS method. The proposed SBDS method is tested with numerical experiments and the performance is compared against boundary discretization methods such as the IBDS and boundary element methods.

Boundary particle method for Laplace transformed time fractional diffusion equations

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

A heat-flux based “building block” approach for solving heat conduction problems

A numerical approximation of the Green’s function equation based on a heat-flux formulation is given. It is derived by assuming as a functional form of the surface heat flux a stepwise variation with space and time. The obtained approximation is very important in investigation of the inverse heat conduction problems (IHCPs) because it gives a convenient expression for the temperature in terms of the heat flux components. Additionally, it is very important for the unsteady surface element (USE) method which is a modern boundary discretization method. Green’s function approximate solution equation (GFASE) also creates ‘naturally’ fixed groups or modules of work elements called “building blocks” that may be added together to obtain space and time values of temperature. In the current case, they are subject to a partial heating by an applied surface heat flux. The “building block” solution can be derived by using the various analytical and numerical approaches available in heat conduction literature though the exact analysis is preferable, as discussed in the text. Poorly-convergent series deriving from Green’s functions approach are replaced by closed-form algebraic solutions.

Unstructured tetrahedral mesh generation technology

We present a robust unstructured tetrahedral mesh generation technology. This technology is a combination of boundary discretization methods, an advancing front technique and a Delaunay-based mesh generation technique. For boundary mesh generation we propose four different approaches using analytical boundary parameterization, interface with CAD systems, surface mesh refinement, and constructive solid geometry. These methods allow us to build a flexible grid generation technology with a user friendly interface.

BOUNDARY PARTICLE METHOD FOR INVERSE CAUCHY PROBLEMS OF INHOMOGENEOUS HELMHOLTZ EQUATIONS

This paper investigates the boundary particle method (BPM) coupled with truncated singular value decomposition (TSVD) regularization technique on the solution of inverse Cauchy problems of inhomogeneous Helmholtz equations. Unlike the other boundary discretization methods, the BPM does not require any inner nodes to evaluate the particular solution, since the method uses the recursive composite multiple reciprocity technique to reduce an inhomogeneous problem to a series of higher-order homogeneous problems. The BPM is particular attractive to solve inverse problems thanks to its truly boundary-only meshless merit. In this study, numerical experiments demonstrate that the BPM in conjunction with the TSVD is highly accurate, computationally efficient and stable for inverse Cauchy problems.

Winkler plate bending problems by a truly boundary-only boundary particle method

This paper makes the first attempt to use the boundary particle method (BPM) to solve the problems of Winkler plate under lateral loading. In this study, we find that the standard fundamental solution does not work well with the BPM. Instead we construct the modified singular fundamental solution, which satisfies the homogeneous governing equation of Winkler plate and is employed in the BPM to calculate the homogeneous solution. Unlike the other boundary discretization methods, the BPM does not require any inner nodes to evaluate the particular solution of inhomogeneous problems, since the method is a truly boundary-only meshfree technique by using the recursive composite multiple reciprocity technique. Our numerical experiments demonstrate efficiency and high accuracy of the BPM in the solution of Winkler plate bending problems.

Boundary discretization using the edge-function method in three dimensional elasticity

The edge function asymptotic boundary discretization method, which generates a partition of the boundary into a finite set of boundary elements, and its application to three-dimensional problems of linear isotropic elasticity are presented. The present solution representation, which is global, is constructed from asymptotic solutions of the Navier equations of elasticity. The unknown parameters are then determined by imposing the boundary conditions separately over each of the boundary elements. A numerical example is included and the results are discussed.