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On the Dynamics of the Boundary Vorticity for Incompressible Viscous Flows
Springer Science and Business Media LLC - Tập 99 Số 2 - 2024
Vladislav Cherepanov, Jian Guo Liu, Zhongmin Qian
A Multiple-Relaxation-Time Lattice Boltzmann Model for General Nonlinear Anisotropic Convection–Diffusion Equations
Springer Science and Business Media LLC - - 2016
Zhenhua Chai, Baochang Shi, Zhaoli Guo
Discrete Kernel Preserving Model for 3D Electron–Optical Phonon Scattering Under Arbitrary Band Structures
Springer Science and Business Media LLC - Tập 81 - Trang 2213-2236 - 2019
Wenqi Yao, Tiao Lu
In Li et al. (J Sci Comput 62:317–335, 2015), we thoroughly investigated the structure of the kernel space of the discrete one-dimensional (1D) non-polar optical phonon (NPOP)-electron scattering matrix, and proposed a strategy to setup grid points so that the uniqueness of the discrete scattering kernel is preserved. In this paper, we extend the above work to the three dimensional (3D) case, and ... hiện toàn bộ
Quasi-A Priori Truncation Error Estimation in the DGSEM
Springer Science and Business Media LLC - Tập 64 - Trang 425-455 - 2014
Gonzalo Rubio, François Fraysse, David A. Kopriva, Eusebio Valero
In this paper we show how to accurately perform a quasi-a priori estimation of the truncation error of steady-state solutions computed by a discontinuous Galerkin spectral element method. We estimate the spatial truncation error using the $$\tau $$ -estimation procedure. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimat... hiện toàn bộ
An h-p Version of the Continuous Petrov–Galerkin Method for Nonlinear Delay Differential Equations
Springer Science and Business Media LLC - Tập 74 - Trang 1091-1114 - 2017
Tingting Meng, Lijun Yi
We investigate an h-p version of the continuous Petrov–Galerkin time stepping method for nonlinear delay differential equations with vanishing delays. We derive a priori error estimates in the $$L^{2}$$ -, $$H^{1}$$ - and $$L^\infty $$ -norm that are completely explicit with respect to the local time steps, the local polynomial degrees, and the local regularity of the exact solution. Moreover, we ... hiện toàn bộ
The application of the locally implicit method to upwind TVD schemes
Springer Science and Business Media LLC - Tập 7 - Trang 339-357 - 1992
Yih Nen Jeng, Uon Jien Payne
The local implicit scheme of Reddyet al. is extended to the minmod and third-order upwind TVD schemes. Numerical tests show that the proposed scheme is stable. In addition, it is found that if the flow field has a dominant direction, setting the iteration sweep to align with this direction can significantly improve the converging speed.
An Improved Local-Min-Orthogonal Method for Finding Multiple Solutions to Nonlinear Elliptic PDEs
Springer Science and Business Media LLC - Tập 92 - Trang 1-23 - 2022
Xianjin Chen, Zhaoxiang Li, Jianxin Zhou
In this paper, motivated by some recent progress in the development of Partial Newton-Correction Method for finding multiple solutions to nonlinear PDEs and by a closer observation to the implementation of the Local Min-Orthogonal (LMO) method developed in 2004, first a new L- $$\bot $$ selection expression is introduced, then the (strict) separation condition and the continuity condition used in ... hiện toàn bộ
A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima
Springer Science and Business Media LLC - Tập 74 - Trang 1314-1324 - 2017
Wenrui Hao
A numerical method for estimating multiple parameter values of nonlinear systems arising from biology is presented. The uncertain parameters are modeled as random variables. Then the solutions are expressed as convergent series of orthogonal polynomial expansions in terms of the input random parameters. Homotopy continuation method is employed to solve the resulting polynomial system, and more imp... hiện toàn bộ
A Kernel-Independent Sum-of-Exponentials Method
Springer Science and Business Media LLC - Tập 93 - Trang 1-35 - 2022
Zixuan Gao, Jiuyang Liang, Zhenli Xu
We propose an accurate algorithm for a novel sum-of-exponentials (SOE) approximation of kernel functions, and develop a fast algorithm for convolution quadrature based on the SOE, which allows an order N calculation for N time steps of approximating a continuous temporal convolution integral. The SOE method is constructed by a combination of the de la Vallée-Poussin sum for a semi-analytical expon... hiện toàn bộ
Entropy Consistent Methods for the Navier–Stokes Equations
Springer Science and Business Media LLC - Tập 63 - Trang 612-631 - 2014
Akmal Nizam Mohammed, Farzad Ismail
The concept of entropy conservation, stability, and consistency is applied to systems of hyperbolic equations to create new flux functions for the scalar and systems of conservation laws. Firstly, Burgers’ equation is modelled, followed by the Navier–Stokes equations. The new models are compared with the pre-existing entropy consistent fluxes at selected viscosity levels; it is found that the syst... hiện toàn bộ
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