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This study aims to simulate the dendritic growth in Stokes flow by iteratively coupling a domain and boundary type meshless method.

A preconditioned phase-field model for dendritic solidification of a pure supercooled melt is solved by the strong-form space-time adaptive approach based on dynamic quadtree domain decomposition. The domain-type space discretisation relies on monomial augmented polyharmonic splines interpolation. The forward Euler scheme is used for time evolution. The boundary-type meshless method solves the Stokes flow around the dendrite based on the collocation of the moving and fixed flow boundaries with the regularised Stokes flow fundamental solution. Both approaches are iteratively coupled at the moving solid–liquid interface. The solution procedure ensures computationally efficient and accurate calculations. The novel approach is numerically implemented for a 2D case.

The solution procedure reflects the advantages of both meshless methods. Domain one is not sensitive to the dendrite orientation and boundary one reduces the dimensionality of the flow field solution. The procedure results agree well with the reference results obtained by the classical numerical methods. Directions for selecting the appropriate free parameters which yield the highest accuracy and computational efficiency are presented.

A combination of boundary- and domain-type meshless methods is used to simulate dendritic solidification with the influence of fluid flow efficiently.

Confronting the unveiled sophisticated structural and physical characteristics of permanent magnets, notably the samarium–cobalt (Sm-Co) alloy, This work aims to introduce a simulation scheme that can link physics-based micromagnetics on the nanostructures and magnetostatic homogenization on the mesoscale polycrystalline structures.

The simulation scheme is arranged in a multiscale fashion. The magnetization behaviors on the nanostructures examined with various orientations are surrogated as the micromagnetic-informed hysterons. The hysteresis behavior of the mesoscale polycrystalline structures with micromagnetic-informed hysterons is then evaluated by computational magnetostatic homogenization.

The micromagnetic-informed hysterons can emulate the magnetization reversal of the parameterized Sm-Co nanostructures as the local hysteresis behavior on the mesostructures. The simulation results of the mesoscale polycrystal demonstrate that the demagnetization process starts from the grain with the largest orientation angle (a) and then propagates to the surrounding grains.

The presented scheme depicts the demand for integrating data-driven methods, as the parameters of the surrogate hysteron intrinsically depend on the nanostructure and its orientation. Further hysteron parameters that help the surrogate hysteron emulate the micromagnetic-simulated magnetization reversal should be examined.

This work provides a novel multiscale scheme for simulating the polycrystalline permanent magnets’ hysteresis while recapitulating the nanoscale mechanisms, such as the nucleation of domains, and domain wall migration and pinning. This scheme can be further extended to simulate the part-level hysteresis considering the mesoscale features.

Current methods for flow field reconstruction mainly rely on data-driven algorithms which require an immense amount of experimental or field-measured data. Physics-informed neural network (PINN), which was proposed to encode physical laws into neural networks, is a less data-demanding approach for flow field reconstruction. However, when the fluid physics is complex, it is tricky to obtain accurate solutions under the PINN framework. This study aims to propose a physics-based data-driven approach for time-averaged flow field reconstruction which can overcome the hurdles of the above methods.

A multifidelity strategy leveraging PINN and a nonlinear information fusion (NIF) algorithm is proposed. Plentiful low-fidelity data are generated from the predictions of a PINN which is constructed purely using Reynold-averaged Navier–Stokes equations, while sparse high-fidelity data are obtained by field or experimental measurements. The NIF algorithm is performed to elicit a multifidelity model, which blends the nonlinear cross-correlation information between low- and high-fidelity data.

Two experimental cases are used to verify the capability and efficacy of the proposed strategy through comparison with other widely used strategies. It is revealed that the missing flow information within the whole computational domain can be favorably recovered by the proposed multifidelity strategy with use of sparse measurement/experimental data. The elicited multifidelity model inherits the underlying physics inherent in low-fidelity PINN predictions and rectifies the low-fidelity predictions over the whole computational domain. The proposed strategy is much superior to other contrastive strategies in terms of the accuracy of reconstruction.

In this study, a physics-informed data-driven strategy for time-averaged flow field reconstruction is proposed which extends the applicability of the PINN framework. In addition, embedding physical laws when training the multifidelity model leads to less data demand for model development compared to purely data-driven methods for flow field reconstruction.