We extend “A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D”, Veerapaneni et al. Journal of Computational Physics, 228(7), 2009 to the case of three dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spec...

We investigate the stability of a fully-implicit, linearly extrapolated Crank-Nicolson (CNLE) time-stepping scheme for finite element spatial discretization of the Navier-Stokes equations. Although presented in 1976 by Baker and applied and analyzed in various contexts since then, all known convergence estimates of CNLE require a time-step restriction. We propose a new linear extrapolation of t...

We study the time-dependent Navier–Stokes equations in context of stochastic finite element discretizations. Specifically, we assume that viscosity is a random field given form generalized polynomial chaos expansion, and use Galerkin method to extend methodology from Kay et al. (2010) [21] into this framework. For resulting problem, explore properties solutions, also compare results with Monte ...

in this paper an efficient dual time implicit approach is used to solve viscous laminar flow around two bodies with general motion. therefore, the grid includes a background grid and two sets of grids around the moving bodies. rotational and translational motions of two bodies are managed separately in this grid arrangement. in this work the overset concept for hybrid grid is used and flow vari...

We compare the performance of the fully coupled Newton–Raphson method with the sequential iteration approach (SIA) for solving the implicit time stepping equations of reactive transport modeling. We formulate the implicit time stepping equations for a demonstration model that incorporates homogeneous equilibrium reactions, i.e. carbonate hydrolysis, and a heterogeneous equilibrium reaction, i.e...

Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend “A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows”, Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general non-axisymmetric vesicle flows in three dimensions. Although the main components of the algorithm are similar in ...

[1] Problems associated with shear zone development in the lithosphere involve features of widely different time scales, since the gradual buildup of stress leads to rapid and localized shear instability. These phenomena have a large stiffness in time domain and cannot be solved efficiently by a single time-integration scheme. This conundrum has forced us to use an adaptive time-stepping scheme...

An implicit energy-decaying modified Crank--Nicolson time-stepping method is constructed for the viscous rotating shallow water equation on plane. Existence, uniqueness, and convergence of semidiscrete solutions are proved by using Schaefer's fixed point theorem $H^2$ estimates discretized hyperbolic--parabolic system. For practical computation, further in space, resulting a fully discrete fini...

The specific objective of this paper is to develop a fully implicit compositional simulator for modeling asphaltene deposition during natural depletion. In this study, a mathematical model for asphaltene deposition modeling is presented followed by the solution approach using the fully implicit scheme. A thermodynamic model for asphaltene precipitation and the numerical methods for performing f...