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71.
Assessment of different reconstruction techniques for implementing the NVSF schemes on unstructured meshes 下载免费PDF全文
Three new far‐upwind reconstruction techniques, New‐Technique 1, 2, and 3, are proposed in this paper, which localize the normalized variable and space formulation (NVSF) schemes and facilitate the implementation of standard bounded high‐resolution differencing schemes on arbitrary unstructured meshes. By theoretical analysis, it is concluded that the three new techniques overcome two inherent drawbacks of the original technique found in the literature. Eleven classic high‐resolution NVSF schemes developed in the past decades are selected to evaluate performances of the three new techniques relative to the original technique. Under the circumstances of arbitrary unstructured meshes, stretched meshes, and uniform triangular meshes, for each NVSF scheme, the accuracies and convergence properties, when implementing the four aforementioned far‐upwind reconstruction techniques respectively, are assessed by the pure convection of several scalar profiles. The numerical results clearly show that New‐Technique‐2 leads to a better performance in terms of overall accuracy and convergence behavior for the 11 NVSF schemes. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
72.
This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second-order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third-order accurate Adams-Moulton method and the second-order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier. 相似文献
73.
Pengzhan Huang Xiaoling Ma Rena Askar 《Mathematical Methods in the Applied Sciences》2016,39(12):3496-3505
This paper presents a superconvergence result of the stationary natural convection equations. The superconvergence result is obtained by applying a coarse mesh projection for finite element approximation. This projection method is actually a postprocessing procedure that constructs a new approximation based on a high order polynomial on coarse mesh, under some regularity assumption. Finally, numerical experiment is presented for testing, which confirms the theoretic analysis. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
74.
Stability prediction for milling process with multiple delays using an improved semi‐discretization method 下载免费PDF全文
Gang Jin Houjun Qi Yujun Cai Qichang Zhang 《Mathematical Methods in the Applied Sciences》2016,39(4):949-958
Milling chatter leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Thus, it is desirable to predict and avoid the onset of this instability. Considering that the stability of milling with variable pitch cutter or tool runout case is characterized by multiple delays, in this paper, an improved semi‐discretization method is proposed to predict the stability lobes for milling processes with multiple delays. Taking the variable pitch milling, for example, a comparisonwith prior methods is conducted to verify the accuracy and efficiency of the proposed approach for the stability prediction both in low and high radial immersion ratios. In addition, the rate of convergence of the proposed method is also evaluated. The results show that the proposed method has high computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
75.
An energy‐preserving Crank–Nicolson Galerkin method for Hamiltonian partial differential equations 下载免费PDF全文
Haochen Li Yushun Wang Qin Sheng 《Numerical Methods for Partial Differential Equations》2016,32(5):1485-1504
A semidiscretization based method for solving Hamiltonian partial differential equations is proposed in this article. Our key idea consists of two approaches. First, the underlying equation is discretized in space via a selected finite element method and the Hamiltonian PDE can thus be casted to Hamiltonian ODEs based on the weak formulation of the system. Second, the resulting ordinary differential system is solved by an energy‐preserving integrator. The relay leads to a fully discretized and energy‐preserved scheme. This strategy is fully realized for solving a nonlinear Schrödinger equation through a combination of the Galerkin discretization in space and a Crank–Nicolson scheme in time. The order of convergence of our new method is if the discrete L2‐norm is employed. An error estimate is acquired and analyzed without grid ratio restrictions. Numerical examples are given to further illustrate the conservation and convergence of the energy‐preserving scheme constructed.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1485–1504, 2016 相似文献
76.
On a nonoverlapping additive Schwarz method for h‐p discontinuous Galerkin discretization of elliptic problems 下载免费PDF全文
Piotr Krzyżanowski 《Numerical Methods for Partial Differential Equations》2016,32(6):1572-1590
The condition number of a discontinuous Galerkin finite element discretization preconditioned with a nonoverlapping additive Schwarz method is analyzed. We improve the result of Antonietti and Houston (J Sci Comput 46 (2011), 124–149), where a bound has been proved for a two‐level nonoverlapping additive Schwarz method with coarse problem using polynomials of degree on a coarse mesh size . In a more general framework, where the concurrency of the algorithm is increased by applying solvers on subdomains smaller than the coarse grid cells, we prove that the condition number of the preconditioned system is where is the coarse space element degree polynomial and is the size of subdomain where local problems are solved in parallel. Our result also extends to the case of discontinuous coefficient, piecewise constant on the coarse grid, for a composite continuous–discontinuous Galerkin discretization. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1572–1590, 2016 相似文献
77.
The time discretization in classes of integro‐differential equations with completely monotonic kernels: Weighted asymptotic convergence 下载免费PDF全文
Da Xu 《Numerical Methods for Partial Differential Equations》2016,32(3):896-935
We consider the time discretization for the solution of the equation with . Here, the operators Lj are densely defined positive self‐adjoint linear operator on a Hilbert space H and have spectral decompositions with respect to a common resolution of the identity in H . The kernel functions , are assumed to be completely monotonic on (0,∞) and locally integrable, but not constant. The considered time discretization method comes from [Da Xu, Science China Mathematics 56 (2013), 395–424], where the backward Euler method is combined with order one convolution quadrature for approximating the integral term. In this article, the convergence properties of the time discretization are given in the weighted and norm, where ρ is a given weighted function. Numerical experiments show the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 896–935, 2016 相似文献
78.
79.
In this paper we propose a fully discretized version of the collocation method applied to integral equations of the first
kind with logarithmic kernel. After a stability and convergence analysis is given, we prove the existence of an asymptotic
expansion of the error, which justifies the use of Richardson extrapolation. We further show how these expansions can be translated
to a new expansion of potentials calculated with the numerical solution of a boundary integral equation such as those treated
before. Some numerical experiments, confirming our theoretical results, are given.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
80.
Jun Zhang 《Numerical Methods for Partial Differential Equations》2000,16(1):1-10
We present a new strategy to accelerate the convergence rate of a high‐accuracy multigrid method for the numerical solution of the convection‐diffusion equation at the high Reynolds number limit. We propose a scaled residual injection operator with a scaling factor proportional to the magnitude of the convection coefficients, an alternating line Gauss‐Seidel relaxation, and a minimal residual smoothing acceleration technique for the multigrid solution method. The new implementation strategy is tested to show an improved convergence rate with three problems, including one with a stagnation point in the computational domain. The effect of residual scaling and the algebraic properties of the coefficient matrix arising from the fourth‐order compact discretization are investigated numerically. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 1–10, 2000 相似文献