The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The p...The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.展开更多
基于光滑粒子流体动力学方法(Smoothed Particle Hydrodynamics,SPH),开展了SPH新算法在蒸发燃烧领域的研究。建立了适用于SPH方法的蒸发数值模型,推导了基于傅立叶热传导公式和菲克扩散定律的SPH离散方程;借鉴VOF方法(Volume of Fluid...基于光滑粒子流体动力学方法(Smoothed Particle Hydrodynamics,SPH),开展了SPH新算法在蒸发燃烧领域的研究。建立了适用于SPH方法的蒸发数值模型,推导了基于傅立叶热传导公式和菲克扩散定律的SPH离散方程;借鉴VOF方法(Volume of Fluid)的思想,提出了SPH粒子的液相质量分数的概念,以有效表征蒸发过程中的相变问题。采用SPH方法对高温环境中单个液滴的蒸发过程进行数值模拟,结果符合D2定律,与理论模型相一致;在强迫对流环境中,液滴的蒸发过程受到对流作用及表面张力的影响,蒸发速率加快;进一步对双液滴在静止、对流环境中的蒸发过程进行数值模拟研究。结果表明,液滴的间距、滴径对多个液滴的蒸发过程影响至关重要,液滴间距至少在两倍的液滴直径以上,相互之间的影响才可以近似忽略。通过本文研究,拓宽了SPH方法在蒸发相变领域的应用范围,研究结果也能够为进一步的燃烧问题研究奠定基础。展开更多
基金Supported by the National Natural Science Foundation of China(11101124 and 11271231)Natural Science Foundation of Shandong Province(ZR2016AM08)National Tackling Key Problems Program(2011ZX05052,2011ZX05011-004)
文摘The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.
文摘基于光滑粒子流体动力学方法(Smoothed Particle Hydrodynamics,SPH),开展了SPH新算法在蒸发燃烧领域的研究。建立了适用于SPH方法的蒸发数值模型,推导了基于傅立叶热传导公式和菲克扩散定律的SPH离散方程;借鉴VOF方法(Volume of Fluid)的思想,提出了SPH粒子的液相质量分数的概念,以有效表征蒸发过程中的相变问题。采用SPH方法对高温环境中单个液滴的蒸发过程进行数值模拟,结果符合D2定律,与理论模型相一致;在强迫对流环境中,液滴的蒸发过程受到对流作用及表面张力的影响,蒸发速率加快;进一步对双液滴在静止、对流环境中的蒸发过程进行数值模拟研究。结果表明,液滴的间距、滴径对多个液滴的蒸发过程影响至关重要,液滴间距至少在两倍的液滴直径以上,相互之间的影响才可以近似忽略。通过本文研究,拓宽了SPH方法在蒸发相变领域的应用范围,研究结果也能够为进一步的燃烧问题研究奠定基础。
