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As the penalized vortex-in-cell (pVIC) method is based on the vorticity-velocity form of the Navier–Stokes equation, the pressure variable is not incorporated in its solution procedure. This is one of the advantages of vorticity-based methods such as pVIC. However, dynamic pressure is an essential flow property in engineering problems. In pVIC, the pressure field can be explicitly evaluated by a pressure Poisson equation (PPE) from the velocity and vorticity solutions. How to specify far-field boundary conditions is then an important numerical issue. Therefore, this paper aims to robustly and accurately determine the boundary conditions for solving the PPE.

This paper introduces a novel non-iterative method for specifying Dirichlet far-field boundary conditions to solve the PPE in a bounded domain. The pressure field is computed using the velocity and vorticity fields obtained from pVIC, and the solid boundary conditions for pressure are also imposed by a penalization term within the framework of pVIC. The basic idea of our approach is that the pressure at any position can be evaluated from its gradient field in a closed contour because the contour integration for conservative vector fields is path-independent. The proposed approach is validated and assessed by a comparative study.

This non-iterative method is successfully implemented to the pressure calculation of the benchmark problems in both 2D and 3D. The method is much faster than all the other methods tested without compromising accuracy and enables one to obtain reasonable pressure field even for small computation domains that are used regardless of a source distribution (the right-hand side in the Poisson equation).

The strategy introduced in this paper provides an effective means of specifying Dirichlet boundary conditions at the exterior domain boundaries for the pressure Poisson problems. It is very efficient and robust compared with the conventional methods. The proposed idea can also be adopted in other fields dealing with infinite-domain Poisson problems.

This paper aims to present harmonic response of magneto‐electro‐elastic cylinder by quasi‐static and fully dynamic electromagnetic theories. The quasi‐static assumption uses magnetic scalar potential whereas magnetic vector potential is employed in a fully dynamic model.

The electric field induced by time varying magnetic field is non‐conservative and can be described by electric scalar potential and magnetic vector potentials.

The magnitude of vector potential is dominant in axial and circumferential direction whereas the magnetic flux density is significant in radial direction. Magnetic scalar potential approach evaluates only the radial component of magnetic flux density and electric field intensity is reasonably the same as that of the magnetic vector potential approach.

Semi‐analytical finite element method is used in this paper and the vector potential is formulated in cylindrical coordinates.

The simulation of magnetic fields with geometric discretization schemes using magnetic vector potentials involves the solution of very large discrete consistently singular curl‐curl systems of equations. Geometric and algebraic multigrid schemes for their solution require intergrid transfer operators of restriction and prolongation that achieve the discrete conservation of integral quantities serving as state‐variables of geometric discretization methods. For non‐conservative restriction operations, a consistency error correction operator related to an algebraic filtering is proposed. Numerical results show the effects of the consistency correction for a non‐nested geometric multigrid method.

An adaptive grid solution method is described for computing the time accurate solution of an unsteady flow problem. The solution method consists of three parts: a grid point redistribution method; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the flow solver. The grid movement technique is a direct curve by curve method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. By design, the temporal coupling procedure provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one‐dimensional shock tube and a two‐dimensional shock vortex interaction. Quantitative comparisons are made between the adaptive solutions, theoretical solutions and numerical solutions computed on stationary grids. Test results demonstrate the good temporal tracking of the solution by the adaptive grid, and the ability of the adaptive method to capture an unsteady solution of comparable accuracy to that computed on a stationary grid containing significantly more grid points than used in the adaptive grid.

Higher energy conversion efficiency of internal combustion engine can be achieved with optimal control of unsteady in-cylinder flow fields inside a direct-injection (DI) engine. However, it remains a daunting task to predict the nonlinear and transient in-cylinder flow motion because they are highly complex which change both in space and time. Recently, machine learning methods have demonstrated great promises to infer relatively simple temporal flow field development. This paper aims to feature a physics-guided machine learning approach to realize high accuracy and generalization prediction for complex swirl-induced flow field motions.

To achieve high-fidelity time-series prediction of unsteady engine flow fields, this work features an automated machine learning framework with the following objectives: (1) The spatiotemporal physical constraint of the flow field structure is transferred to machine learning structure. (2) The ML inputs and targets are efficiently designed that ensure high model convergence with limited sets of experiments. (3) The prediction results are optimized by ensemble learning mechanism within the automated machine learning framework.

The proposed data-driven framework is proven effective in different time periods and different extent of unsteadiness of the flow dynamics, and the predicted flow fields are highly similar to the target field under various complex flow patterns. Among the described framework designs, the utilization of spatial flow field structure is the featured improvement to the time-series flow field prediction process.

The proposed flow field prediction framework could be generalized to different crank angle periods, cycles and swirl ratio conditions, which could greatly promote real-time flow control and reduce experiments on in-cylinder flow field measurement and diagnostics.

The application of numerical techniques to the solution of practical problems which exist in rubber technology is described. Structures and components in the form of reinforced rubber shells are widely used in industry and prediction of their performance is complicated by both the anisotropic nature of composite construction and the incompressible behaviour of the basic material. A layered shell element is developed for the solution of such problems with general anisotropic behaviour independently permitted in each layer. The approach adopted permits the easy location of reinforcement patterns. Numerical solution is based on a single field formulation by eliminating at integrating point level the Lagrange multiplier imposing the incompressible constraint. Large deformation, including large rotation, behaviour is accommodated and a total Lagrangian solution process is adopted. The code developed permits the simulation of non‐conservative loading and its versatility is demonstrated by the solution of some practical examples.

This article presents a locally conservative projection method which aims to preserve the integral of a function and one operator among grad, div, or curl.

After a theoretical description of the projection methods, the locally conservative projection is analytically tested and compared with the orthogonal method. In the second part, the implementation of the methods is described, and improvements are proposed. An industrial application of the present work, consisting in a magneto-thermal coupled problem, is then presented.

The implementation of the conservative method is simpler than the implementation of the orthogonal method while presenting similar behaviour in terms of accuracy and conservation.

The locally conservative method is extended to curl-conform and div-conform elements. Furthermore, three-dimensional studies are proposed.

Presents an implementation of continuation methods in the context of a code for flexible multibody systems analysis. These systems are characterized by the simultaneous presence of elastic deformation terms and rigid constraints. In our formulation, the latter terms are introduced by an augmented Lagrangian technique, resulting in the presence of Lagrange multipliers in the set of unknowns, together with displacement and rotation associated terms. Essential aspects for a successful implementation are discussed: e.g. the selection of an appropriate metric for computing the path following constraint, a flexible description of control parameters which accounts for conservative and nonconservative loads, imposed displacements and imposed temperatures (dilatation effects), and the inclusion of second order derivatives of rigid constraints in the Jacobian. A large set of examples is presented, with the objective of evaluating the numerical effectiveness of the implemented schemes.

The jet impingement usually accompanying large interface movement is studied by the in-house solver MLParticle-SJTU based on the modified moving particle semi-implicit (MPS) method, which can provide more accurate pressure fields and deformed interface shape. The comparisons of the pressure distribution and the shape of free surface between the presented numerical results and the analytical solution are investigated. The paper aims to discuss these issues.

To avoid the instability in traditional MPS, a modified MPS method is employed, which include mixed source term for Poisson pressure equation (PPE), kernel function without singularity, momentum conservative gradient model and highly precise free surface detection approach. Detailed analysis on improved schemes in the modified MPS is carried out. In particular, three kinds of source term in PPE are considered, including: particle number density (PND) method, mixed source term method and divergence-free method. Two typical kernel functions containing original kernel function with singularity and modified kernel function without singularity are analyzed. Three kinds of pressure gradient are considered: original pressure gradient (OPG), conservative pressure gradient (CPG) and modified pressure gradient (MPG). In addition, particle convergence is performed by running the simulation with various spatial resolutions. Finally, the comparison of the pressure fields by the modified MPS and by SPH is presented.

The modified MPS method can provide a reliable pressure distribution and the shape of the free surface compared to the analytical solution in a steady state after the water jet impinging on the wall. Specifically, mixed source term in PPE can give a reasonable profile of the shape of free surface and pressure distribution, while PND method adopted in the traditional MPS is not stable in simulation, and divergence-free method cannot produce rational pressure field near the wall. Two kernel functions show similar pressure field, however, the kernel function without singularity is preferred in this case to predict the profile of free surface and pressure on the wall. The shape of free surface by CPG and MPG is agreement with the analytical solution, while a great discrepancy can be observed by OPG. The pressure peak by MPG is closer to the analytical solution than that by CPG, while the pressure distribution on the right hand side of the pressure peak by latter is better match with the analytical solution than that by former. Besides, fine spatial resolution is necessary to achieve a good agreement with analytical results. In addition, the pressure field by the modified MPS is also quite similar to that by SPH, and this can further validate the reliable of current modified MPS.

The present modified MPS appears to be a stable and reliable tool to deal with the impinging jet flow problems involving large interface movement. Mixed source term in PPE is superior to PND adopted in the traditional MPS and divergence-free method. The kernel function without singularity is preferred to improve the computational accuracy in this case. CPG is a good choice to obtain the shape of free surface and the pressure distribution by jet impingement.

The paper seeks to do the following. To provide an expression of the electromagnetic power flow that is alternative to the Poynting's theorem expression, overcomes its postulate feature, and is particularly suitable for electric circuit elements.

The paper proceeds from fundamental electromagnetic laws and, independently of Poynting's formulation, follows an approach that generalize established double formulations of the electrostatic and magnetostatic energies.

The paper proposes a compact and straightforward expression of the electromagnetic power flow based on the fundamental electromagnetic field sources, i.e. charge and current densities.

The achieved expression confirms Poynting's expression in the case of electric elements, overcoming its arbitrariness, generalizes previous partial results by other authors, deduced via the Poynting's power balance.

Is promising in the computation of power flow electromagnetic devices connected in electrical circuits, i.e. for coupled problems where the analysis of electromagnetic system interfaced to electric circuits is required. Due to its simple structure and straightforward deduction it has educational value to demonstrate the expressions of the electric power in circuit elements.