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 Galerkin finite… More >

Xiang-YangLi¹, Shang-Hua Teng², Peng-Jun Wan³

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 97-116, 2001, DOI:10.3970/cmes.2001.002.097

Abstract To conduct numerical simulations by finite element methods, we often need to generate a high quality mesh, yet with a smaller number of elements. Moreover, the size of each of the elements in the mesh should be approximately equal to a given size requirement. Li et al. recently proposed a new method, named biting, which combines the strengths of advancing front and sphere packing. It generates high quality meshes with a theoretical guarantee. In this paper, we show that biting squares instead of circles not only generates high quality meshes but also has the following advantages. It is easier to… More >

Xiaofeng Yang¹, Ashley J. James^1,2

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 65-96, 2007, DOI:10.3970/fdmp.2007.003.065

Abstract An arbitrary Lagrangian-Eulerian (ALE) method for interfacial flows with insoluble surfactants is presented. The interface is captured using a coupled level set and volume of fluid method, which takes advantage of the strengths of both the level set method and the volume of fluid method. By directly tracking the surfactant mass, the method conserves surfactant mass, and prevents surfactant from diffusing off the interface. Interfacial area is also tracked. To accurately approximate the interfacial area, the fluid interface is reconstructed using piece-wise parabolas. The surfactant concentration, which determines the local surface tension through an equation of state, is then computed… More >

CMC-Computers, Materials & Continua, Vol.48, No.1, pp. 43-55, 2015, DOI:10.3970/cmc.2015.048.043

Abstract This study proposed a modified unstructured kinetic model for sodium gluconate fermentation by Aspergillus niger. Four specific growth rate equations (Monod, Tessier, Contois, and logistic) were considered in the biomass growth equation. The growth, instantaneous biomass concentration, instantaneous product, and substrate concentration were considered in the equations of product formation and substrate consumption. Option parameters were introduced to determine the form of the unstructured model. A double-nested optimization strategy was proposed to optimize the option and kinetic parameters. The proposed unstructured kinetic model based on the estimated optimal parameters efficiently simulated sodium gluconate fermentation. The obtained option parameters of the… More >