Search Results (77)

Fully implicit simulation of multiphase flow in porous media requires repeated solution of large, sparse, nonsymmetric Jacobian systems, where linear solvers and preconditioners often dominate the computational cost. In field-scale models with strong well controls and well–reservoir coupling, bottom-hole pressure (BHP) constraints may introduce slowly converging pressure-related error modes that are not fully represented by pressure-only constrained pressure residual (CPR) preconditioning. This paper develops a Schur-consistent graphics processing unit (GPU) implementation of constrained pressure residual with wells and algebraic multigrid (CPRW-AMG) for the Open Porous Media (OPM) Flow simulator. The method augments the pressure coarse space with one auxiliary BHP unknown per active well while preserving a reservoir-only fine-level Krylov system. The pressure–BHP coarse operator is constructed from the same assembled effective reservoir Jacobian used by the Krylov matrix–vector product and the GPU diagonal incomplete lower–upper (DILU) smoother, avoiding inconsistent treatment of well contributions between fine and coarse levels. A GPU-resident sparse update strategy refreshes well-related coarse entries, and the NVIDIA AMGX library is used for the scalar coarse solve. Benchmarks on SPE9, SPE10, Sleipner, and Norne cover small well-coupled, highly heterogeneous carbon dioxide storage and field-realistic reservoir models. Compared with CPU CPRW-AMG, the GPU implementation reduces total runtime by factors of 1.69–8.78 and achieves linear-solve speedups of up to 17.96×. Compared with GPU CPR-AMG, the performance benefit is case-dependent, indicating that CPRW-AMG is most effective when the reduction in well-induced slow error modes compensates for the additional coarse-level cost. Full article

Time-varying mesh stiffness (TVMS) is a primary contributor to gear noise, vibration and harshness (NVH). Accurate implementation of the lubrication effect on the TVMS is often neglected. This work presents a numerical lubricated contact stiffness extraction method by combining the lubricant film and elastic compliances through rigid-body separation for spur gears. A deformation datum for infinite line contacts is defined using Weber’s local elastic deformation of gear teeth, resolving inconsistent treatments in the literature. A novel apparent transient damping coefficient is extracted using transient multigrid elastohydrodynamic (EHL) simulations. At high load and low speed, the EHL contact stiffness approaches the analytical local elastic stiffness, whereas at low load and high speed, it deviates by up to an order of magnitude. The stiffness linearisation is compared directly against fixed-separation EHL solutions, and force reconstruction confirms recovery of the full transient contact force. The results show that lubricant film compliance can significantly alter the EHL contact stiffness under low-load/high-speed conditions, which is relevant to dynamic mesh force fluctuations in high-speed transmissions. Thus, accurate lubricant effects must be included for reliable NVH predictions in such cases. Full article

The accurate representation of frontal zones—characterized by sharp scalar gradients—remains a critical challenge in regional objective analysis and data assimilation, particularly when utilizing sparse or stochastically distributed observations. This study evaluates the efficacy of Multiquadric Radial Basis Functions (RBFs) as a high-order alternative to standard spatial mapping operators frequently used in machine learning atmospheric emulators. We contrast the performance of the regularized, $C^{\infty }$-continuous RBF approach against nearest neighbor and linear mesh interpolation schemes using both synthetic baroclinic wave profiles and an operational case study of the intense extratropical cyclone that impacted the East Coast of North America in mid-March 1993. To mitigate characteristic boundary artifacts and geometric clipping in bounded regional domains, we implement a targeted numerical stabilization framework combining localized boundary mirroring with four-corner domain anchoring. Our quantitative results demonstrate that the optimized RBF framework substantially improves gradient fidelity and reduces Root Mean Square Error across a wide range of observation densities. Furthermore, we evaluate the computational scalability of RBFs on high-performance computing architectures, demonstrating how Algebraic Multigrid solvers and Graphics Processing Unit acceleration mitigate the foundational $O\left(N^3\right)$ computational bottleneck. We conclude that RBF interpolation provides a physically consistent, analytically differentiable manifold that addresses the derivative discontinuities of traditional linear methods, offering a stable pre-processing framework for high-resolution meteorological analysis and machine learning optimization. Full article

Multibody dynamics (MBD) simulations involving hundreds to thousands of bodies give rise to large-scale, sparse, and structurally indefinite linear systems. Traditional direct solvers incur prohibitive memory and computational costs, while iterative methods suffer from slow convergence due to severe ill-conditioning. This paper proposes HPI-MBD, a hybrid preconditioned iterative framework. It combines an algebraic multigrid (AMG) for global error smoothing with a block Jacobi preconditioner tailored to the kinematic constraint graph. The framework exploits graph topology to construct a block-diagonal Schur complement approximation, incorporates Tikhonov regularisation for redundant constraints, and maintains $\mathcal{O}\left(n\right)$ work per iteration, where n is the number of degrees of freedom. A rigorous spectral analysis supports the problem-size independent convergence of the Minimal Residual (MINRES) solver. Evaluated on five benchmark systems with ${10}^4$ to ${10}^6$ degrees of freedom, the HPI-MBD achieves speedups up to $12.7\times$ and memory reductions up to 68% against MA57, with comparable gains against PARDISO. All solutions maintain relative residuals below ${10}^{-6}$. Comparisons against ILU(0)-preconditioned Generalised Minimal Residual (GMRES), Finite Element Tearing and Interconnecting method (FETI-1), and a block-Jacobi-only variant confirm the essential role of AMG. The framework exhibits near-linear scalability and strong parallel efficiency on up to 32 processors, along with robust performance under redundant constraints and varying time step sizes. These results position HPI-MBD as a scalable, memory-efficient alternative for real-time simulation in virtual prototyping, robotics, and biomechanics. Full article

This article reviews the linear solvers available in OpenFOAM and assesses their impact on the convergence behaviour of the SIMPLE algorithm. The discretisation of transport equations in CFD results in large and sparse linear systems, for which the choice of linear solver strongly influences the computational time. Although the solver does not change the final discrete solution, the difference in speed and robustness between the solvers can be more than one order of magnitude. A brief overview is given concerning how the velocity and pressure fields are decoupled in OpenFOAM, followed by a detailed review of the main linear solver families, including direct methods, basic iterative methods, multigrid methods and Krylov subspace methods, with attention to their practical strengths and weaknesses. The performance of the most advanced solvers is evaluated on a full-scale non-reacting kiln case consisting of 2.3 million cells. The pressure-corrector equation is identified as the main bottleneck in the SIMPLE algorithm. The conjugate gradient (CG) solver with a multigrid (MG) preconditioner is found to be the fastest and most stable method, achieving speed-ups of up to a factor of 7 compared to the slower advanced methods. Using MG as a preconditioner also improves the robustness of the Bi-CGStab method. Full article

This paper investigates co-continuous structures in immiscible polymer blends through three-dimensional (3D) computational calculations based on a multiphase phase-field equation for fluid flow. The mathematical model describes phase separation with the Cahn–Hilliard (CH) equation and fluid motion with the incompressible Navier–Stokes (NS) equations. Both polymers are treated as Newtonian viscous fluids, and the model includes surface tension, viscosity, and volume fraction effects. A semi-implicit finite difference method (FDM) solves the CH equation, and a projection method maintains the incompressibility of the flow field. Multigrid techniques solve the nonlinear systems efficiently. In addition, a connectivity-based detection algorithm determines whether a phase forms a connected structure that reaches all boundaries of the numerical domain. The numerical results show that the morphology changes from a droplet–matrix structure to a co-continuous structure as the volume fraction increases. The interfacial area per unit volume reaches a local maximum near the transition between these two regimes. Full article

The three-dimensional borehole-to-surface transient electromagnetic (BSTEM) method plays a critical role in resolving subsurface conductivity structures under complex geological conditions. However, its application is often constrained by the high computational costs associated with large-scale simulations and fine temporal resolution. In this study, a time-parallel forward modeling strategy is employed by integrating the finite volume method (FVM) with the Multigrid Reduction-in-Time (MGRIT) algorithm. Maxwell’s equations are discretized in space using unstructured octree meshes, while the MGRIT algorithm enables parallelism along the time axis through coarse–fine temporal grid hierarchy and multilevel iterative correction. Numerical experiments on synthetic and field-scale models demonstrate that the MGRIT-based solver significantly reduces computational time compared to conventional direct solvers, particularly when a large number of processors are utilized. In a field-scale hematite mine model, the MGRIT-based solver reduces the total runtime by more than 40% while maintaining numerical accuracy. The method exhibits parallel scalability and is especially advantageous in problems involving a large number of time channels, where simultaneous time-step updates offer substantial performance gains. These results confirm the effectiveness and robustness of the proposed approach for large-scale 3D TEM simulations under complex conditions and provide a practical foundation for future applications in high-resolution electromagnetic modeling and imaging. Full article

Lubrication plays a crucial role in reducing gear surface damage and defects such as pitting, wear, and scuffing; therefore, analyzing the influence of lubrication is essential for preventing such failures in gear transmission systems. To this end, the dynamic properties of gear systems were examined, leading to the creation of a thermal elastohydrodynamic lubrication (TEHL) model for the line contact of involute spur gears. This model utilizes a multigrid method to calculate the oil film pressure and thickness. Subsequently, models for meshing stiffness, normal oil film stiffness, and overall normal stiffness were developed using energy methods and lubrication theory. Ultimately, a dynamic model of the spur gear system that incorporated lubrication effects was developed to examine how different operating conditions affect dynamic transmission error, vibration velocity, and dynamic meshing force. The findings revealed that when considering the TEHL effect, the dynamic transmission error along the gear meshing line increases, while both the vibration velocity and dynamic meshing force exhibit a decrease. Furthermore, as speed and load intensify, the amplitudes of dynamic transmission error, vibration velocity, and dynamic meshing force also rise. Notably, an increase in the initial viscosity of the lubricating oil correlates with a decrease in the fluctuation of dynamic transmission error, while the variations in vibration velocity and dynamic meshing force remain relatively insignificant. Full article

A review of the development of grid technologies and corresponding numerical approaches based on the lattice Boltzmann method (LBM) is performed in the present study. The history of the algorithmic development and practical applications is presented and followed by a short introduction of the basic theory of LBM, especially the classic lattice Bhatnagar–Gross–Krook LBGK D2Q9 model. In reality, all the different grid technologies reported aim to solve one but very important problem, the local grid refinement, which largely influences the stability, efficiency, accuracy, and flexibility of the conventional LBM. The improvement of these numerical properties after employing various grid technologies is analyzed. Several grid technologies, such as body-fitted grid, multigrid, non-uniform rectangular grid, quadtree Cartesian square grid, unstructured grid and meshless discrete points, as well as the corresponding numerical approaches are compared and discussed. Full article

In this paper, we investigate how adaptive time-integration strategies can be effectively combined with parallel-in-time numerical methods for solving systems of ordinary differential equations. Our focus is particularly on their influence on tolerance proportionality. We examine various grid-refinement strategies within the multigrid reduction-in-time (MGRIT) framework. Our results show that a simple adjustment to the original refinement factor can substantially improve computational stability and reliability. Through numerical experiments on standard test problems using the XBraid library, we demonstrate that parallel-in-time solutions closely match their sequential counterparts. Moreover, with the use of multiple processors, computing time can be significantly reduced. Full article

Cylindrical roller bearings are widely used in industrial machinery, automotive systems, and aerospace applications, where their reliability directly affects the performance and safety of mechanical systems. The fatigue life of cylindrical roller bearings is significantly affected by their elastohydrodynamic lubrication condition, with variations potentially reaching multiple times. However, conventional quasi-static models often neglect lubrication effects. This study establishes a quasi-static analysis model for cylindrical roller bearings that incorporates the effects of elastohydrodynamic lubrication by integrating elastohydrodynamic lubrication theory with the Lundberg–Palmgren life model. The isothermal line contact elastohydrodynamic lubrication equations are solved using the multigrid method, and the contact load distribution is determined through nonlinear iterative techniques to calculate bearing fatigue life. Taking the N324 support bearing on the main shaft of an SFW250-8/850 horizontal hydro-generator as an example, the influences of radial load, inner race speed, and lubricant viscosity on fatigue life are comparatively analyzed. Experimental validation is conducted under both light-load and heavy-load operating conditions. The results demonstrate that elastohydrodynamic lubrication markedly increases contact loads, leading to a reduced predicted fatigue life compared with that of the De Mul model (which ignores lubrication). The proposed lubrication-integrated model achieves an average deviation of 5.3% from the experimental data, representing a 16.1% improvement in prediction accuracy over the De Mul model. Additionally, increased rotational speed and lubricant viscosity accelerate fatigue life degradation. Full article

The underwater corner reflector is a “concave” elastic structure, and its acoustic echo exhibits large elastic loss, which affects its practical use. To study the acoustic echo elastic loss characteristics of underwater corner reflectors, based on the characteristics of small concave elastic structures of underwater corner reflectors, theoretical calculations were performed using the method of a combination of finite element and boundary element. Taking the underwater rigid corner reflector as the benchmark, the acoustic echo differences between similar types of underwater elastic corner reflectors were compared. The regular acoustic echo elastic loss of underwater corner reflectors was analyzed, and verified through pool experiments. The results show that, whether single-grid or multi-grid corner reflector, the actual acoustic echoes of underwater corner reflectors conform to the characteristics of elastic bodies, which differ significantly from rigid bodies and exhibit obvious elastic loss. The elastic loss mainly manifests as reduced target strength (TS), narrower directional pattern width, and poorer frequency stability of target strength, which is detrimental to practical use. This study provides assistance in proposing targeted methods to suppress elastic loss. Full article

The structure and memory organization of graphics processor units (GPUs) manufactured by NVIDIA and the use of CUDA programming technology to solve computational fluid dynamics (CFD) problems is reviewed and discussed. The potential of using a general-purpose GPU to solve fluid dynamics problems is examined. The code optimization with the utilization of various memory types is considered. Some CFD benchmark problems focused on simulation of viscous incompressible fluid flows are solved on GPUs. Consideration is given to the application of the finite volume method and projection method. Programming implementation of various components of the computational procedure, solution of Poisson equation for pressure and multigrid method to solve the system of algebraic equations, is provided. By using meshes of varying resolutions and different techniques for dividing up the input data into blocks, the speedup of the GPU solution is compared to the CPU approach. Full article

A new high-order hybrid method integrating neural networks and corrected finite differences is developed for solving elliptic equations with irregular interfaces and discontinuous solutions. Standard fourth-order finite difference discretization becomes invalid near such interfaces due to the discontinuities and requires corrections based on Cartesian derivative jumps. In traditional numerical methods, such as the augmented matched interface and boundary (AMIB) method, these derivative jumps can be reconstructed via additional approximations and are solved together with the unknown solution in an iterative procedure. Nontrivial developments have been carried out in the AMIB method in treating sharply curved interfaces, which, however, may not work for interfaces with geometric singularities. In this work, machine learning techniques are utilized to directly predict these Cartesian derivative jumps without involving the unknown solution. To this end, physics-informed neural networks (PINNs) are trained to satisfy the jump conditions for both closed and open interfaces with possible geometric singularities. The predicted Cartesian derivative jumps can then be integrated in the corrected finite differences. The resulting discrete Laplacian can be efficiently solved by fast Poisson solvers, such as fast Fourier transform (FFT) and geometric multigrid methods, over a rectangular domain with Dirichlet boundary conditions. This hybrid method is both easy to implement and efficient. Numerical experiments in two and three dimensions demonstrate that the method achieves fourth-order accuracy for the solution and its derivatives. Full article

We consider the problem of computed tomography (CT). This ill-posed inverse problem arises when one wishes to investigate the internal structure of an object with a non-invasive and non-destructive technique. This problem is severely ill-conditioned, meaning it has infinite solutions and is extremely sensitive to perturbations in the collected data. This sensitivity produces the well-known semi-convergence phenomenon if iterative methods are used to solve it. In this work, we propose a multigrid approach to mitigate this instability and produce fast, accurate, and stable algorithms starting from unstable ones. We consider, in particular, symmetric Krylov methods, like lsqr, as smoother, and a symmetric projection of the coarse grid operator. However, our approach can be extended to any iterative method. Several numerical examples show the performance of our proposal. Full article