A new matrix-free implicit iteration algorithm based on finite volume method for simulating groundwater seepage flows

An effective and reliable numerical method is developed to solve the three-dimensional incompressible Navier-Stokes equations and to investigate fluid flows in three-dimensional branching tubes. The proposed numerical method is developed by the artificial compressible method. It uses a third-order upwind finite volume method to discretize convection terms and a second-order finite volume to discretize viscous terms. A diagonal dominated alternating direction implicit scheme (DDADI) coupling with an implicit residual smoothing is used to achieve a larger CFL number for time marching. The fluid flows in Y-shape and T-shape tubes are simulated. The effects of Reynolds number, branching flow ratio, branching angle, and corner type of branching tube on flow field behaviors are investigated. The vortex length and circulation zone are also discussed.

Numerical scheme for solving the Richard’s equation based on finite volume model with unstructured mesh and implicit dual-time stepping

Preconditioning methods for compressible flow CFD codes: Revisited

The existence of shock–turbulent boundary layer interactions lead to very complicated flow phenomena and pose a challenge for numerical simulation. In this paper, two turbulence models, the Baldwin–Lomax (B–L) model and the Johnson–King (J–K) model, which were originally developed for simple external flow simulation, are modified to model complex high-speed internal separated flows. The full Navier–Stokes solver used in this paper is based on a cell-centered finite volume method and multistepping time marching scheme. Both implicit residual smoothing and local time stepping techniques are incorporated to accelerate the convergence rate. To ensure the numerical stability with the present explicit scheme, a point-implicit treatment to the source term in the ordinary differential equation (ODE) of the J–K model has been developed and has proved to be very effective in modeling such a complex flow. An arc-bump channel flow case has been studied. Comparisons of computed results with experimental data show that the present solver, with the modified turbulence models, predicts the shock and the flow separation very well. The J–K model is found to predict the size of the separation bubble with a higher accuracy. © 1998 John Wiley & Sons, Ltd.

This paper aims to investigate the effects of moisture migration and groundwater seepage on the heat transfer capacity of ground heat exchangers in stratified soils. A three-dimensional unsteady groundwater flow and heat transport model was established using finite volume method. Sixteen cases with different model considerations and initial soil conditions were simulated based on the proposed model. A group of 8 cases considering only transverse moisture migration and another group considering both transverse and longitudinal moisture migration were compared. The heat and moisture fields after 30 days of operation reveal that considering the change of saturation caused by vertical moisture transfer, the soil temperature field will be affected, but borehole outlet temperature was less influenced. The absolute value of outlet temperature difference between corresponding cases in the two groups is only about 0.2 °C. The position of groundwater seepage and arrangement of unsaturated soil layers with different degrees of saturation on heat transfer capacity of vertical ground heat exchanger were further explored. The results show that the longitudinal moisture migration would be made more influential by the existence of seepage layer, because the average relative deviation of inlet and outlet temperature difference between the corresponding cases of Group 1 and Group 2 was 1.34% when setting seepage layer and was 0.44% when without seepage layer. Heat transfer performance of borehole heat exchanger is also affected by the location of seepage layer. The average relative deviation of inlet and outlet temperature difference between the reference case and cases with seepage in the top, middle and bottom layers is 34.18%, 25.08% and 16.82%, respectively. The arrangement of unsaturated soil layers also has a certain effect. When the soil layer with low degree of saturation is located in the upper layer of soil, heat transfer capacity is better.

Noisy gradient algorithms have emerged as one of the most popular algorithms for distributed optimization with massive data. Choosing proper step-size schedules is an important task to tune in the algorithms for good performance. For the algorithms to attain fast convergence and high accuracy, it is intuitive to use large step-sizes in the initial iterations when the gradient noise is typically small compared to the algorithm-steps, and reduce the step-sizes as the algorithm progresses. This intuition has been confirmed in theory and practice for stochastic gradient descent. However, similar results are lacking for other methods using approximate gradients. This paper shows that the diminishing step-size strategies can indeed be applied for a broad class of noisy gradient algorithms. Our analysis framework is based on two classes of systems that characterize the impact of the step-sizes on the convergence performance of many algorithms. Our results show that such step-size schedules enable these algorithms to enjoy the optimal rate. We exemplify our results on stochastic compression algorithms. Our experiments validate fast convergence of these algorithms with the step decay schedules.

Adaptive disturbance observer-based dual-loop integral-type fast terminal sliding mode control for micro spacecraft and its gimbal tracking device

In this work, an extension of the discrete unified gas-kinetic scheme (DUGKS) to gas–liquid phase change problems is proposed based on the conservative Allen–Cahn phase-field model. The kinetic framework of the DUGKS for gas–liquid phase change problems comprises three components: the conservative Allen–Cahn phase-field equation to describe the interface evolution, the Navier–Stokes equations for fluid flow, and the energy equation for the temperature field. To model the phase change, a source term is introduced based on the heat conduction balance across the interface. By applying Chapman–Enskog analysis, these kinetic equations can be correctly recovered to the corresponding macroscopic equations. The DUGKS approach, which integrates the strengths of the lattice Boltzmann method and the finite volume method, can capture the non-equilibrium phenomenon of phase change more precisely and simulate under the non-uniform mesh with high accuracy. The main contribution of this work lies in formulating a gas–liquid phase change phase-field model by embedding a physically consistent source term into the conservative Allen–Cahn equation under the framework of the DUGKS, enabling an accurate description of the interfacial dynamics during phase change. Including one-dimensional Stefan problem, the evaporation of the stationary droplet, the falling evaporating droplet under gravity in a container, and the saturated film boiling, four benchmark cases are conducted to validate the proposed models and methods. It is demonstrated that the present method can accurately capture the interface dynamics and simulate the gas–liquid phase change problems.

A compressible lattice Boltzmann finite volume model for high subsonic and transonic flows on regular lattices

Efficient and robust prediction of internal temperature distribution and boundary heat flux in participating media by using the Kalman smoothing technique

This work shows that, by adequately rewriting the one-dimensional convection-diffusion equation in a diffusional form, all the usual numerical procedures, that is, the finite element, finite volume and finite difference procedures, lead to the same and optimal steady-state stencil for numerical solutions. Additionally, a lumped capacitance (mass) matrix first-order time integration technique is presented. The resulting scheme, expressed with a transient, special lumped capacitance matrix (PMGV or prevailing main grid value method), was used to solve the problem of onedimensional transient saturated soil solute transport. A benchmark problem with analytical solution, representing a moving concentration front in a saturated soil was solved by both the diffusional method and by the Two-Step Taylor-Galerkin (TSTG) finite element method. The diffusional (PMGV) method proved itself to be an excellent option for solving advection dominated problems such as soil solute transport problems. The simulation results showed that the explicit PMGV scheme leads to the same accuracy as the TSTG scheme. The TSTG scheme shows numerical dispersion while the diffusional method showed false diffusion. However, the stability region for the PMGV is broader. The PMGV scheme is more effective than the TSTG in problems involving either low Pe numbers or high Pe numbers, if mesh refinement is made.

Iterative learning control (ILC) involves a trade-off between perfect, fast attenuation of iteration-invariant disturbances and amplification of iteration-varying ones. The aim of this paper is to develop a nonlinear ILC framework that achieves fast convergence, robustness, and low converged error values in ILC. To this end, the method includes a deadzone nonlinearity in the learning update, which uses the difference in amplitude characteristics of repeating and varying disturbances to modify the learning gain for each error sample. A criterion for monotonic convergence of the nonlinear ILC algorithm is provided, which is used in combination with system measurements to select suitable design parameters. The proposed algorithm is validated using simulations, in which fast convergence to low error values is demonstrated.

As an extension of the classic rigid registration algorithm-Iterative Closest Point (ICP) algorithm, this paper proposes a new non-rigid ICP algorithm to match two point sets. Each point in the data set is supposed to match to the model set via an affine transformation. The proposed registration model is built up with a regularization term based on their average affine transformation. For each iteration of our algorithm, firstly correspondences between two point sets are built by the nearest-point search. Then the non-rigid transform parameters between two correspondence point sets are estimated by the proposed method in the closed form. Finally the average affine transformation is updated. A set of challenging data including single and overlapping chromosome images are tested which have significant local non-rigid transformations. Experimental results demonstrate our algorithm has higher accuracy and faster rate of convergence than other algorithms.

Parabolic partial differential equation with small parameter in x direction and different small parameter in t direction is considered. This kind of problem leads to boundary layer phenomena in both side of x direction and bottom side of t direction. The analytical solution changes rapidly near three boundary layer. Firstly, the asymptotic solution with order one for all small parameter is studied. The analytical solution is approximated by the degenerate solution and three boundary layer functions. Secondly, non-equidistant mesh partitions both in x direction and t direction are constructed according to Shishkin's idea. The domain is divided into the outside boundary layer and the boundary layer. Thirdly, traditional finite volume method is applied by integrating the equation over the control volume. The discretized equation is derived. Asymptotic solution is used for the outside boundary layer, while finite volume method is applied for three boundary layers. Finally, numerical example is studied to demonstrate the accuracy of the present method.

This paper addresses the key issue of calculating fluxes at the control-volume interfaces when finite-volumes are employed for the solution of partial differential equations. This calculation becomes even more significant when unstructured grids are used, since the flux approximation involving only two grid points is no longer correct. Two finite volume methods with the ability in dealing with unstructured grids, the EbFVM-Element-based Finite Volume Method and the MPFA-Multi-Point Flux Approximation are presented, pointing out the way the fluxes are numerically evaluated. The methods are applied to a porous media flow with full permeability tensors and non-orthogonal grids and the results are compared with analytical solutions. The results can be extended to any diffusion operator, like heat and mass diffusion, in anisotropic media.