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The paper considers an implementation of an adaptive computational grid constructing algorithm in a numerical solution of the one-dimensional forward magnetotelluric sounding problem (the Tikhonov–Cagniard problem). The numerical solution of the problem is realized by a method of local integral equations which was proposed by the authors previously. The adaptive computational grid construction is based on geometrical principles of optimizing a piecewise constant interpolant of the electrical conductivity function to be approximated. Numerical experiments are carried out to study and illustrate the effectiveness of the combined method. The algorithm is tested on the Kato–Kikuchi model with a known exact solution.

This paper studies the algorithm of the adaptive grid and fuzzy interacting multiple model (AGFIMM) for maneuvering target tracking, while focusing on the problems of the fixed structure multiple model (FSMM) algorithm’s cost-efficiency ratio being not high and the Markov transition probability of the interacting multiple model (IMM) algorithm being difficult to determine exactly. This algorithm realizes the adaptive model set by adaptive grid adjustment, and obtains each model matching degree in the model set by fuzzy logic inference. The simulation results show that the AGFIMM algorithm can effectively improve the accuracy and cost-efficiency ratio of the multiple model algorithm, and as a result is suitable for engineering applications.

Ground filtering is crucial for airborne Light Detection and Ranging (LiDAR) data post-processing. The progressive triangulated irregular network densification (PTD) algorithm and its variants outperform others in accuracy, stability, and robustness, using grid-based seed point selection, TIN construction, and iterative rules for ground point identification. However, these methods still face limitations in removing low points and accurately preserving terrain details, primarily due to their sensitivity to grid size. To overcome this issue, a novel PTD filtering algorithm based on an adaptive grid (AGPTD) was proposed. The main contributions of the proposed method include an outlier removal method using a radius outlier removal algorithm and Kd-tree, a method for establishing an adaptive two-level grid based on point cloud density and terrain slope, and an adaptive selection method for angle and distance thresholds in the iterative densification processing. The performance of the AGPTD algorithm was assessed based on widely used benchmark datasets. Results show that the AGPTD algorithm outperforms the classical PTD algorithm in retaining ground feature points, especially in reducing Type I error and average total error significantly. In comparison with other advanced algorithms developed in recent years, the novel algorithm showed the lowest average Type I error, the minimal average total error, and the greatest average Kappa coefficient, which were 1.11%, 2.28%, and 90.86%, respectively. Additionally, the average accuracy, precision, and recall of AGPTD were 97.69%, 97.52%, and 98.98%, respectively.

Cavitation is a widespread and detrimental phenomenon in hydraulic machinery, therefore, it requires to be accurately predicted. In this study, large eddy simulation (LES), scale-adaptive simulation (SAS) and grid-adaptive simulation (GAS) are employed to investigate the unsteady cavitating flow around a NACA0009 hydrofoil. The prediction accuracy of GAS, SAS, both using the shear-stress transport (SST) k — ω model as baseline turbulence model, is validated by comparing with experimental and LES results. The cavity behaviors and turbulence fields are analyzed systematically. Results show that the GAS gives a more reasonable turbulent viscosity and accurately predicts the periodic evolution of typical vortical structures of cavitating flow, such as tip leakage vortex cavitation, tip separation vortex cavitation, leading-edge cavitation, and trailing-edge vortex. The time-averaged cavity volume, volume fluctuation amplitude, and characteristic frequencies of cavities predicted by the GAS are very closed to the LES, while the SAS fails to accurately capture these cavity characteristics. Furthermore, the local trace criterion is applied to extract the vortical structures and to analyze the swirling patterns of the tip leakage vortex. Multi-scale vortical structures in LES are well identified by local trace criterion. The prediction accuracy of the SAS method for small-scale vortical structures, such as the vortex shedding on the suction side and the vortex rope around the tip leakage vortex, is obviously insufficient, while the GAS has a higher accuracy in predicting vortex shedding. The tip leakage vortex and induced vortex extracted from GAS are also closer to that of LES in both swirling patterns and scale.

Gas pipeline leakage will result in casualties and property losses if not detected in time. Conventional leakage localization methods usually rely on dense grid distribution, leading to high computational costs. This study proposes a time-reversal-based adaptive grid generation approach to enhance computational efficiency in pipeline leakage localization. The method introduces a resolution adjustment parameter to optimize captured signals, allowing for adaptive grid concentration in leakage areas based on energy distribution. Based on this principle, three steps—including signal adjustment computation, adaptive grid generation computation, and conventional TR localization computation based on the adaptive grids—are introduced. Then, an experimental study is conducted on a 55.8 m PVC pipeline with piezoceramic transducers, capturing negative pressure wave signals from four leakage points. The results demonstrate that the proposed approach maintains comparable localization accuracy while reducing the number of grids and localization time to only 0.6% and 2.4% of those required by conventional uniform grid methods, respectively. The findings demonstrate that the proposed method offers a computationally efficient and accurate solution for real-time pipeline leakage monitoring.

A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration, exploiting an arbitrary number of hierarchical fidelity levels, i.e., performance evaluations coming from different models, solvers, or discretizations, characterized by different accuracy. The method is intended to accurately predict the design performance while reducing the computational effort required by simulation-driven design (SDD) to achieve the global optimum. The overall MF prediction is evaluated as a low-fidelity trained surrogate corrected with the surrogates of the errors between consecutive fidelity levels. Surrogates are based on stochastic radial basis functions (SRBF) with least squares regression and in-the-loop optimization of hyperparameters to deal with noisy training data. The method adaptively queries new training data, selecting both the design points and the required fidelity level via an active learning approach. This is based on the lower confidence bounding method, which combines the performance prediction and the associated uncertainty to select the most promising design regions. The fidelity levels are selected considering the benefit-cost ratio associated with their use in the training. The method’s performance is assessed and discussed using four analytical tests and three SDD problems based on computational fluid dynamics simulations, namely the shape optimization of a NACA hydrofoil, the DTMB 5415 destroyer, and a roll-on/roll-off passenger ferry. Fidelity levels are provided by both adaptive grid refinement and multi-grid resolution approaches. Under the assumption of a limited budget for function evaluations, the proposed MF method shows better performance in comparison with the model trained by high-fidelity evaluations only.

The higher order Haar wavelet method (HOHWM) is used with a nonuniform grid to solve nonlinear partial differential equations numerically. The Burgers’ equation, the Korteweg–de Vries equation, the modified Korteweg–de Vries equation and the sine–Gordon equation are used as model equations. Adaptive as well as nonadaptive nonuniform grids are developed and used to solve the model equations numerically. The numerical results are compared to the known analytical solutions as well as to the numerical solutions obtained by application of the HOHWM on a uniform grid. The proposed methods of using nonuniform grid are shown to significantly increase the accuracy of the HOHWM at the same number of grid points.

The multiscale finite volume method for discrete fracture modeling in highly heterogeneous porous media is developed. Multiscale methods are sensitive to the heterogeneity contrasts in both matrix and fracture networks. To resolve this, efficient algorithms for generating adaptive unstructured coarse grids are devised. First, primal coarse grids are independently constructed for the matrix and lower dimensional fractures. Then, flexible dual coarse grids are generated based on the fracture and matrix permeability features. Since the proposed algorithms employ the equivalent graph of unstructured grids, the same coarse grid generation strategy is applied for the fractures and matrix domains. Permeability-adapted coarse grids significantly improve the monotonicity behavior of MSFV method in highly heterogeneous fractured porous media. The performance of the method is assessed through several challenging test cases with highly heterogeneous permeability field in both fractures and matrix domain. Numerical results indicate that the extended MSFV method with adaptive unstructured coarse grids is a significant development for accurate flow simulation in heterogeneous fractured media using DFM approach.

Seeking to better understand the physical phenomena underlying detonation wave propagation through small holes (especially the phenomenon of detonation re-initiation or its failure), we investigated the propagation of a detonation wave along a tube filled with a hydrogen-oxygen mixture diluted with argon, in the presence of obstacles with a small orifice hole. Numerical simulations were performed in a two-dimensional domain using adaptive mesh refinement and by solving compressible Euler equations for multiple thermally perfect species with a reactive source term. A premixed mixture of H2:O2:Ar at a ratio 2:1:7 at 10.0 kPa and 298 K was used in a 90 mm diameter tube with a detonation wave travelling from one end. We found that a single orifice placed at 200 mm from one end of the tube, with varying diameters of 6, 10, 14, 16, 18, 30, and 50 mm, showed an initial decoupling of the detonation wave into a shockwave and flame front. The detonation wave fails to propagate along the tube for orifice diameters less than λ, while it propagates by different re-initiation pathways for orifice diameters greater than λ, where λ is the cell-width for regular detonation propagation.

This paper introduces a continuous finite element model to simulate fluid flow-bedform interaction problems. The approach utilizes a non-oscillatory finite element algorithm to compute the fluid dynamics by solving the complete Navier–Stokes equations. Additionally, it addresses the evolution of the fluid–bedform interface as a consequence of spatially non-balanced sediment fluxes through the solution of a conservation equation for the erodible layer thickness. A sign preservation algorithm is particularly relevant for landform tracking because a positive definite thickness of the erodible sediment layer is essential to model the interaction between evolving cohesionless sediment layers and rigid beds. The fluid/terrain interface is explicitly captured through a surface tracking methodology. First, new nodes fitting the interface are incorporated into the finite element mesh; then, elements beneath this interface are deactivated, while intersected elements are restructured to get a mesh composed exclusively of tetrahedral elements. Numerical experiments demonstrate capabilities of the method by exploring relevant problems related with civil engineering, such as the evolution of trenches and the scour of a submerged pile.