Biao Wang¹, Yuxiang Peng^1,*, Wenhua Xu²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.3, pp. 1-2, 2024, DOI:10.32604/icces.2024.012061

Abstract The damage process of ship structures under near-field underwater explosions involves strong nonlinear coupling effects of multiple media, and its numerical simulation poses a serious challenge to traditional numerical algorithms. Based on previous research, this article first establishes a highly compressible multiphase flow numerical calculation model based on the high-precision Discontinuous Galerkin Method (DGM) and a ship elastic-plastic damage dynamic model based on the meshless Reproducing Kernel Particle Method (RKPM). Furthermore, we develop an algorithm for grid-independent dynamic expansion of cracks. Based on this, the Boundary Data Immersion Method (BDIM) is used to couple the More >

Zhaoxu Lian¹,Wenbin Wu^2,*, Moubin Liu^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.011054

Abstract The underwater explosion (UNDEX) could cause the fatal damage of naval ships and submarines in the naval battle, and seriously threaten their combat capability [1]. The UNDEX process is very complicated, including the propagation and reflection of the shock wave, formation and collapse of cavitation zone, trainset dynamic structural response and so on [2]. In this paper, we develop the three-dimensional Discontinuous Galerkin method (DGM) model for simulating the propagation of incident shock loading in fluid domain. The pressure cutoff model is employed to deal with the cavitation effect due to the reflection of the More >

Zhen Wang^{1, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.1, pp. 353-376, 2020, DOI:10.32604/cmes.2020.08776 - 01 April 2020

Abstract In this paper, a special case of nonlinear time fractional cable equation is studied. For the equation defined on a bounded domain, the existence, uniqueness, and regularity of the solution are firstly studied. Furthermore, it is numerically studied via the weighted and shifted Grünwald difference (WSGD) methods/the local discontinuous Galerkin (LDG) finite element methods. The derived numerical scheme has been proved to be stable and convergent with order O(∆t² + h^k+1), where ∆t, h, k are the time stepsize, the spatial stepsize, and the degree of piecewise polynomials, respectively. Finally, a numerical experiment is presented to verify the More >

P.A. Trapper¹, P.Z. Bar-Yoseph²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 19-47, 2014, DOI:10.3970/cmes.2014.103.019

Abstract The space-time discontinuous Galerkin method for multi-dimensional nonlinear hyperbolic systems is enhanced with a generalized technique for splitting a flux vector that is not limited to the homogeneity property of the flux. This technique, based on the flux’s characteristic decomposition, extends the scope of the method’s applicability to a wider range of problems, including elastodynamics. The method is used for numerical solution of a number of representative problems based on models of vibrating string and vibrating rod that involve the propagation of a sharp front through the solution domain. More >

M. Dumbser¹, D.S. Balsara²

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.3, pp. 301-334, 2009, DOI:10.3970/cmes.2009.054.301

Abstract In this article we use the new, unified framework of high order one-step P_NP_M schemes recently proposed for inviscid hyperbolic conservation laws by Dumbser, Balsara, Toro, and Munz (2008) in order to solve the viscous and resistive magnetohydrodynamics (MHD) equations in two and three space dimensions on unstructured triangular and tetrahedral meshes. The P_NP_M framework uses piecewise polynomials of degree N to represent data in each cell and piecewise polynomials of degree M ≥ N to compute the fluxes and source terms. This new general machinery contains usual high order finite volume schemes (N = 0) and discontinuous… More >

Donghuan Liu¹, Xiaoping Zheng^1,2, Yinghua Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.3, pp. 263-300, 2009, DOI:10.3970/cmes.2009.039.263

Abstract A discontinuous Galerkin (DG) finite element method for the heat conduction problems with local high gradient and thermal contact resistance is presented. The DG formulation is constructed by employing the stabilization term and the Bassi-Rebay numerical flux term. The stabilization term is defined by a penalization of the temperature jump at the interface. By eliminating the penalization term of the temperature jump in the region of local high gradient and imperfect contact interfaces, the present DG method is applied to solve problems involving local high gradient and thermal contact resistance where the numerical flux is… More >

Chyou-Chi Chien, Tong-Yue Wu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 213-226, 2001, DOI:10.3970/cmes.2001.002.213

Abstract This study presents a novel computational method for implementing the time finite element formulation for the equations of linear structural dynamics. The proposed method adopts the time-discontinuous Galerkin method, in which both the displacement and velocity variables are represented independently by second-order interpolation functions in the time domain. The solution algorithm derived utilizes a predictor/multi-corrector technique that can effectively obtain the solutions for the resulting system of coupled equations. The numerical implementation of the time-discontinuous Galerkin finite element method is verified through several benchmark problems. Numerical results are compared with exact and accepted solutions from More >