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

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 >

Rina Okuyama¹, Naoto Mitsume², Hideki Fujii¹, Hideaki Uchida^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 949-965, 2021, DOI:10.32604/cmes.2021.015773

Abstract As the number of automobiles continues to increase year after year, the associated problem of traffic congestion has become a serious societal issue. Initiatives to mitigate this problem have considered methods for optimizing traffic volumes in wide-area road networks, and traffic-flow simulation has become a focus of interest as a technique for advance characterization of such strategies. Classes of models commonly used for traffic-flow simulations include microscopic models based on discrete vehicle representations, macroscopic models that describe entire traffic-flow systems in terms of average vehicle densities and velocities, and mesoscopic models and hybrid (or multiscale)… More >

Zhen Wang^{1, *}

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

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 >

Hongying Huang, Dehao Yu

The International Conference on Computational & Experimental Engineering and Sciences, Vol.17, No.2, pp. 65-66, 2011, DOI:10.3970/icces.2011.017.065

Abstract In this paper, we apply the coupling of local discontinuous Galerkin(LDG) and natural boundary element (NBE) methods to solve a class of exterior transmission problems in the plane. As a consequence, the main features of LDG and NBEM are maintained and hence the coupled approach benefits from the advantages of both methods. Referring to cite{Gatica2010}, we employ LDG subspaces whose functions are continuous on the coupling boundary. The continuity can be implemented either directly. In this way, the normal derivative becomes the only boundary unknown, and hence the total number of unknown functions is reduced 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 >

Dongdong Wang^1,2, Yue Sun², Ling Li²

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.1, pp. 57-82, 2009, DOI:10.3970/cmes.2009.045.057

Abstract A discontinuous Galerkin meshfree formulation is proposed to solve the potential and elasticity problems of composite material where the material interface has to be appropriately modeled. In the present approach the problem domain is partitioned into patches or sub-domains and each patch holds the same material properties. The discretized meshfree particles within a patch are classified as one particle group. Various patches occupied by different particle groups are then linked using the discontinuous Galerkin formulation where an averaged interface flux or traction is constructed based on the fluxes or tractions computed from the adjacent patches. 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 >