Zifei Meng¹, Pengnan Sun^1,*, Yang Xu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.31, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.011674

Abstract DNS simulations on incompressible flows with high Reynolds number using meshfree methods remain an enduring challenge to be addressed. In the present work, we attempt to use a high-order SPH scheme (TENO-SPH) to make DNS simulations on high Reynolds number flows. To investigate this, several spatial reconstructions are applied under the Riemann-ALE-SPH framework, and their performances are compared. Particularly, the accuracy of SPH is significantly enhanced by WENO and TENO reconstructions. For free surface flows, we implement a Lagrangian TENO-SPH to reproduce these flows at different Reynolds numbers. More importantly, to make DNS simulations, the More >

Zhenhua Jiang^1,*, Xi Deng^2,3, Xin Zhang¹, Chao Yan¹, Feng Xiao⁴, Jian Yu¹

FDMP-Fluid Dynamics & Materials Processing, Vol.20, No.10, pp. 2183-2204, 2024, DOI:10.32604/fdmp.2024.053231 - 23 September 2024

Abstract Shock waves, characterized by abrupt changes in pressure, temperature, and density, play a significant role in various materials science processes involving fluids. These high-energy phenomena are utilized across multiple fields and applications to achieve unique material properties and facilitate advanced manufacturing techniques. Accurate simulations of these phenomena require numerical schemes that can represent shock waves without spurious oscillations and simultaneously capture acoustic waves for a wide range of wavelength scales. This work suggests a high-order discontinuous Galerkin (DG) method with a finite volume (FV) subcell limiting strategies to achieve better subcell resolution and lower numerical More >

W. M. Abd-Elhameed^1,2,*, Asmaa M. Alkenedri²

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 955-989, 2021, DOI:10.32604/cmes.2021.013603 - 19 February 2021

Abstract This paper is dedicated to implementing and presenting numerical algorithms for solving some linear and nonlinear even-order two-point boundary value problems. For this purpose, we establish new explicit formulas for the high-order derivatives of certain two classes of Jacobi polynomials in terms of their corresponding Jacobi polynomials. These two classes generalize the two celebrated non-symmetric classes of polynomials, namely, Chebyshev polynomials of third- and fourth-kinds. The idea of the derivation of such formulas is essentially based on making use of the power series representations and inversion formulas of these classes of polynomials. The derived formulas More >

Tingjin Liu^1,2, Siyuan Zheng³, Xinwei Tang^1,2,3,*, Yichao Gao⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.3, pp. 545-560, 2019, DOI:10.32604/cmes.2019.05043

Abstract Based on the modified scale boundary finite element method and continued fraction solution, a high-order doubly asymptotic transmitting boundary (DATB) is derived and extended to the simulation of vector wave propagation in complex layered soils. The high-order DATB converges rapidly to the exact solution throughout the entire frequency range and its formulation is local in the time domain, possessing high accuracy and good efficiency. Combining with finite element method, a coupled model is constructed for time-domain analysis of underground station-layered soil interaction. The coupled model is divided into the near and far field by the… More >

Xiaojing Liu^1,2, Jizeng Wang¹, Youhe Zhou¹

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 433-446, 2015, DOI:10.3970/cmes.2015.107.433

Abstract Based on the approximation scheme for a L²-function defined on a three-dimensional bounded space by combining techniques of boundary extension and Coiflet-type wavelet expansion, a modified wavelet Galerkin method is proposed for solving three-dimensional Poisson problems with various boundary conditions. Such a wavelet-based solution procedure has been justified by solving five test examples. Numerical results demonstrate that the present wavelet method has an excellent numerical accuracy, a fast convergence rate, and a very good capability in handling complex boundary conditions. More >

C.M.T. Tien¹, N. Thai-Quang¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.4, pp. 301-340, 2015, DOI:10.3970/cmes.2015.105.301

Abstract In this study, we present a numerical discretisation scheme, based on a direct fully coupled approach and compact integrated radial basis function (CIRBF) approximations, to simulate viscous flows in regular/irregular domains. The governing equations are taken in the primitive form where the velocity and pressure fields are solved in a direct fully coupled approach. Compact local approximations, based on integrated radial basis functions, over 3-node stencils are introduced into the direct fully coupled approach to represent the field variables. The present scheme is verified through the solutions of several problems including Poisson equations, Taylor-Green vortices More >

C.M.T. Tien¹, N. Thai-Quang¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.6, pp. 425-469, 2015, DOI:10.3970/cmes.2015.104.425

Abstract In this paper, we propose a three-point coupled compact integrated radial basis function (CCIRBF) approximation scheme for the discretisation of second-order differential problems in one and two dimensions. The CCIRBF employs integrated radial basis functions (IRBFs) to construct the approximations for its first and second derivatives over a three-point stencil in each direction. Nodal values of the first and second derivatives (i.e. extra information), incorporated into approximations by means of the constants of integration, are simultaneously employed to compute the first and second derivatives. The essence of the CCIRBF scheme is to couple the extra… More >

C.M.T. Tien¹, N. Pham-Sy¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.4, pp. 251-304, 2015, DOI:10.3970/cmes.2015.104.251

Abstract This paper presents a high-order coupled compact integrated RBF (CC IRBF) approximation based domain decomposition (DD) algorithm for the discretisation of second-order differential problems. Several Schwarz DD algorithms, including one-level additive/ multiplicative and two-level additive/ multiplicative/ hybrid, are employed. The CCIRBF based DD algorithms are analysed with different mesh sizes, numbers of subdomains and overlap sizes for Poisson problems. Our convergence analysis shows that the CCIRBF two-level multiplicative version is the most effective algorithm among various schemes employed here. Especially, the present CCIRBF two-level method converges quite rapidly even when the domain is divided into… More >

M.D. Campos¹, E.C. Romão²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.3, pp. 139-154, 2014, DOI:10.3970/cmes.2014.103.139

Abstract The objective of this paper aims to present a numerical solution of high accuracy and low computational cost for the three-dimensional Burgers equations. It is a well-known problem and studied the form for one and two-dimensional, but still little explored numerically for three-dimensional problems. Here, by using the High-Order Finite Difference Method for spatial discretization, the Crank-Nicolson method for time discretization and an efficient linearization technique with low computational cost, two numerical applications are used to validate the proposed formulation. In order to analyze the numerical error of the proposed formulation, an unpublished exact solution More >

T.-T. Hoang-Trieu¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.6, pp. 485-516, 2013, DOI:10.3970/cmes.2013.091.485

Abstract In this paper, compact local integrated radial basis function (IRBF) stencils reported in [Mai-Duy and Tran-Cong (2011) Journal of Computational Physics 230(12), 4772-4794] are introduced into the finite-volume / subregion - collocation formulation for the discretisation of second-order differential problems defined on rectangular and non-rectangular domains. The problem domain is simply represented by a Cartesian grid, over which overlapping compact local IRBF stencils are utilised to approximate the field variable and its derivatives. The governing differential equation is integrated over non-overlapping control volumes associated with grid nodes, and the divergence theorem is then applied to More >