Renal Cell Carcinoma in von Hippel–Lindau Disease—From Tumor Genetics to Novel Therapeutic Strategies

  • Kim E
  • Zschiedrich S
N/ACitations
Citations of this article
16Readers
Mendeley users who have this article in their library.

Abstract

The objectives of this study are to investigate the third order accuracy and linear stability of the lattice Boltzmann method (LBM) with the two-relaxation-time collision operator (LTRT) for the advection-diffusion equation (ADE) and compare the LTRT model with the single-relaxation-time (LBGK) model. While the LBGK has been used extensively, the LTRT appears to be a more flexible model because it uses two relaxation times. The extra relaxation time can be used to improve solution accuracy and/or stability. This study conducts a third order Chapman-Enskog expansion on the LTRT to recover the macroscopic differential equations up to the third order. The dependency of third order terms on the relaxation times is obtained for different types of equilibrium distribution functions (EDFs) and lattices. By selecting proper relaxation times, the numerical dispersion can be significantly reduced. Furthermore, to improve solution accuracy, this study introduces pseudo-velocities to develop new EDFs to reduce the second order numerical diffusion. This study also derives stability domains based on the lattice Peclet number and Courant number for different types of lattices, EDFs and different values of relaxation times, while conducting linear stability analysis on the LTRT. Numerical examples demonstrate the improvement of the LTRT solution accuracy and stability by selecting proper relaxation times, lattice Peclet number and Courant number. ?? 2008 Elsevier Ltd. All rights reserved.

Cite

CITATION STYLE

APA

Kim, E., & Zschiedrich, S. (2018). Renal Cell Carcinoma in von Hippel–Lindau Disease—From Tumor Genetics to Novel Therapeutic Strategies. Frontiers in Pediatrics, 6. https://doi.org/10.3389/fped.2018.00016

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free