Diffuse interface method for simulation of the chemical vapor deposition of pyrolytic carbon: Aspects of the mathematical formulation

Abstract

SUMMARYThe present work is inspired by Anderson et al. (Phys. D Nonlinear Phenom. 2000; 135(1-2):175-194) and Noll (http://www.math.cmu.edu/wn0g/noll) and falls in the conceptual line of the Ginzburg-Landau class of first-order phase-transition models based on the concept of phase-field parameter. Trying to keep the exposition as much general as possible, we develop below a thermodynamically consistent rationalization of the physical process of (anisotropic) deposition of pyrolytic carbon from a gas phase. The derivation line we follow is well established in the field of the modern continuum physics. From the covariance of the first principle of thermodynamics, the second Newton's law and the Liouville's theorem with respect to the one-dimensional Lie groups of transformations, the balance laws for the temperature, linear momentum and density are formulated. This system of partial differential equations is comprehended further by the constitutive laws for the phase field, the stress, and the heat and entropy fluxes obtained in a form consistent with the Clausius-Duhem understanding of the second law. The result referred to as a local, strongly coupled initial boundary value problem of chemical vapor deposition (IBVP-CVD) constitutes the general mathematical description of the CVD process. The weak form of isotropic IBVP-CVD is then derived and discretized by means of the discontinuous Galerkin method. At the end of the paper, we also derive the weak formulations for the local lifting operators that provide the stabilization mechanism for the discontinuous Galerkin discretization scheme.

Numerical methods for energy flux of temperature diffusion equation on unstructured meshes

“…These are two-point formulae. It is evident that (10) and (11) are first-order accurate. It is shown from (10) that approximating *u/*l is independent of the position of the auxiliary point 3.…”

“…When the cell nodes are at the material interface, the accuracy of unknowns is not satisfactory. As for more methods of flux approximation, the readers are referred to [10][11][12][13][14][15][16].…”

Multiphase Field Modeling Chemical Vapor Infiltration of SiC/SiC Composite

“…As a diffusive interface method, phase field method has been regarded as one of the most promising tool to model complex microstructure evolution involving topology changing such as interfaces/domain boundaries propagation, merging and splitting in free boundary problem. Based on our previous work on phase field modeling SiC chemical vapor deposition [3,4], a multiphase field model is formulated to simulate the codeposition of Si, SiC and C from Methyltrichlorosilane(MTS) during CVI processing.…”

Numerical modeling of carbon‐based material systems and related topics

“…The minisymposium attracted 28 participants from eight countries. Contributions included in this special issue either directly deal with manufacturing and performance of carbon-based composites or consider more general issues that are relevant not only to carbon-based composites but also to a wider class of heterogeneous materials.The first two papers [1,2] are concerned with numerical modeling of chemical vapor depositionthe leading technology for production of carbon-carbon composite materials. Both contributions explore the same kind of phase field methodology to solve the free boundary value problem of chemical deposition, but there are distinctive differences in the form of the local balance equations and in the discretization techniques employed.…”

“…The first two papers [1,2] are concerned with numerical modeling of chemical vapor depositionthe leading technology for production of carbon-carbon composite materials. Both contributions explore the same kind of phase field methodology to solve the free boundary value problem of chemical deposition, but there are distinctive differences in the form of the local balance equations and in the discretization techniques employed.…”