Chebyshev finite spectral method with extended moving grids

A Chebyshev finite spectral method on non-uniform meshes is proposed. An equidistribution scheme for two types of extended moving grids is used to generate grids. One type is designed to provide better resolution for the wave surface, and the other type is for highly variable gradients. The method has high-order accuracy because of the use of the Chebyshev polynomial as the basis function. The polynomial is used to interpolate the values between the two non-uniform meshes from a previous time step to the current time step. To attain high accuracy in the time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme is used. To avoid numerical oscillations caused by the dispersion term in the Korteweg-de Vries （KdV） equation, a numerical technique on non-uniform meshes is introduced. The proposed numerical scheme is validated by the applications to the Burgers equation （nonlinear convectiondiffusion problems） and the KdV equation （single solitary and 2-solitary wave problems）, where analytical solutions are available for comparisons. Numerical results agree very well with the corresponding analytical solutions in all cases.

A NONCONFORMING ANISOTROPIC FINITE ELEMENT APPROXIMATION WITH MOVING GRIDS FOR STOKES PROBLEM

This paper is devoted to the five parameters nonconforming finite element schemes with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. We show that this element has anisotropic behavior and derive anisotropic error estimations in some certain norms of the velocity and the pressure based on some novel techniques. Especially through careful analysis we get an interesting result on consistency error estimation, which has never been seen for mixed finite element methods in the previously literatures.

A baroclinic typhoon model with a moving multi-nested grid and variational adjustment initialisationI. Numerical method

A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, split scheme and time integration.

An intelligent control method based on artificial neural network for numerical flight simulation of the basic finner projectile with pitching maneuver

In this paper,an intelligent control method applying on numerical virtual flight is proposed.The proposed algorithm is verified and evaluated by combining with the case of the basic finner projectile model and shows a good application prospect.Firstly,a numerical virtual flight simulation model based on overlapping dynamic mesh technology is constructed.In order to verify the accuracy of the dynamic grid technology and the calculation of unsteady flow,a numerical simulation of the basic finner projectile without control is carried out.The simulation results are in good agreement with the experiment data which shows that the algorithm used in this paper can also be used in the design and evaluation of the intelligent controller in the numerical virtual flight simulation.Secondly,combined with the real-time control requirements of aerodynamic,attitude and displacement parameters of the projectile during the flight process,the numerical simulations of the basic finner projectile’s pitch channel are carried out under the traditional PID(Proportional-Integral-Derivative)control strategy and the intelligent PID control strategy respectively.The intelligent PID controller based on BP(Back Propagation)neural network can realize online learning and self-optimization of control parameters according to the acquired real-time flight parameters.Compared with the traditional PID controller,the concerned control variable overshoot,rise time,transition time and steady state error and other performance indicators have been greatly improved,and the higher the learning efficiency or the inertia coefficient,the faster the system,the larger the overshoot,and the smaller the stability error.The intelligent control method applying on numerical virtual flight is capable of solving the complicated unsteady motion and flow with the intelligent PID control strategy and has a strong promotion to engineering application.

Simulation of flows with moving contact lines on a dual-resolution Cartesian grid using a diffuse-interface immersed-boundary method

In this paper, we investigate flows with moving contact lines on curved solid walls on a dual-resolution grid using a diffuse-interface immersed-boundary（DIIB） method. The dual-resolution grid, on which the flows are solved on a coarse mesh while the interface is resolved on a fine mesh, was shown to significantly improve the computational efficiency when simulating multiphase flows. On the other hand, the DIIB method is able to resolve dynamic wetting on curved substrates on a Cartesian grid, but it usually requires a mesh of high resolution in the vicinity of a moving contact line to resolve the local flow. In the present study, we couple the DIIB method with the dual-resolution grid, to improve the interface resolution for flows with moving contact lines on curved solid walls at an affordable cost. The dynamic behavior of moving contact lines is validated by studying drop spreading, and the numerical results suggest that the effective slip length λ_n can be approximated by 1.9Cn, where Cn is a dimensionless measure of the thickness of the diffuse interface. We also apply the method to drop impact onto a convex substrate, and the results on the dual-resolution grid are in good agreement with those on a single-resolution grid. It shows that the axisymmetric simulations using the DIIB method on the dual-resolution grid saves nearly 60% of the computational time compared with that on a single-resolution grid.

Numerical Simulation of Compressible Vortical Flows Using a ConservativeUnstructured-GridAdaptive Scheme

A two-dimensional numerical scheme for the compressible Euler equations is presented and applied here to the simulation of exemplary compressible vortical flows.The proposed approach allows to perform computations on unstructured moving grids with adaptation,which is required to capture complex features of the flowfield.Grid adaptation is driven by suitable error indicators based on theMach number and by element-quality constraints as well.At the new time level,the computational grid is obtained by a suitable combination of grid smoothing,edge-swapping,grid refinement and de-refinement.The grid modifications-including topology modification due to edge-swapping or the insertion/deletion of a new grid node-are interpreted at the flow solver level as continuous(in time)deformations of suitably-defined node-centered finite volumes.The solution over the new grid is obtained without explicitly resorting to interpolation techniques,since the definition of suitable interface velocities allows one to determine the new solution by simple integration of the Arbitrary Lagrangian-Eulerian formulation of the flow equations.Numerical simulations of the steady oblique-shock problem,of the steady transonic flow and of the start-up unsteady flow around the NACA 0012 airfoil are presented to assess the scheme capabilities to describe these flows accurately.

NUMERICAL SIMULATION OF SCOURING PROCESS UNDER SPILLWAY

The scour problem under spillway has received a lot of attention in the past decades. For such a complicated problem, most numerical modeling presented only dealt with the water flows in equilibrium scour pools without considering the changing topography of the riverbed. In this paper, the dynamic process is handled with moving grids, and the governing equations are solved using finite volume method with colocated variable arrangement on boundary-fitted non-orthogonal grids. The results show that the given method is efficient, with which the variation of flow parameters, such as mean velocity and mean pressure, etc., can be computed correctly.

Dispersive Shallow Water Wave Modelling.Part II:Numerical Simulation on a Globally Flat Space

In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be very efficient for the hyperbolic part of equations.The particularity of our study is that we develop an adaptive numerical model using moving grids.Moreover,we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation.Moreover,this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed(numerical)problem.