The pressure equation, generated while solving the incompressible Navier–Stokes equations with the segregated iterative algorithm such as PISO, produces a series of linear equation systems as the time step advances. In this paper, we target at accelerating the iterative solution of these linear systems by improving their initial guesses. We propose a weighted group extrapolation method to obtain a superior initial guess instead of a general one, the solution of the previous linear equation system. In this method, the previous solutions that are used to extrapolate the predicted solutions are carefully organized to address the oscillatory solution on each grid. The proposed method uses a weighted average of the predicted solutions as the new initial guess to avoid over extrapolating. Three numerical test results show that the proposed method can accelerate the iterative solution of most linear equation systems and reduce the simulation time up to 61.3%.

This paper focuses on the design, analysis, and multi-objective optimization of a novel 5-degrees of freedom (DOF) double-driven parallel mechanism. A novel 5-DOF parallel mechanism with two double-driven branch chains is proposed, which can serve as a machine tool. By installing two actuators on one branch chain, the proposed parallel mechanism can achieve 5-DOF of the moving platform with only three branch chains. Afterwards, analytical solution for inverse kinematics is derived. The 5 $\times$ 5 homogeneous Jacobian matrix is obtained by transforming actuator velocities into linear velocities at three points on the moving platform. Meanwhile, the workspace, dexterity, and volume are analyzed based on the kinematic model. Ultimately, a stage-by-stage Pareto optimization method is proposed to solve the multi-objective optimization problem of this parallel mechanism. The optimization results show that the workspace, compactness, and dexterity of this mechanism can be improved efficiently.

Accuracy and performance are key issues for CFD simulation. How to meet the specific accuracy requirements, as well as the optimal simulation performance, is always the research hotspot. This paper presents a general theory of Mesh-Order Independence that is used to guide the configuration of two of the most critical control parameters in a concrete CFD simulation process: grid spacing and discretization order. A concept of optimal mesh-order independent pair which can meet both accuracy and performance requirements at the same time is proposed and analyzed. To find the optimal Mesh-order independent pair, the Mesh-Order Independence is applied to high order FEM simulation, and the specific process and key technologies are detailed. Test and results of two benchmark cases, the Laplace equation and the Helmholtz equation, show that the Mesh-order theory proposed in this paper provides an important guidance for the grid spacing selection and discretization order configuration in practical simulation, especially in the case of high precision requirements. Specifically, only 6 pre-runs with low discretization orders and coarse meshes are needed for the both cases to have a prediction accuracy of more than 70%. INDEX TERMS Mesh-Order independence, grid spacing, discretization order, high-order FEM, CFD.

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