Related papers: Novel numerical analysis for simulating the genera…
In this paper, an efficient numerical technique for the time-fractional telegraph equation is proposed. The aim of this paper is to use a relatively new type of B-spline called the cubic trigonometric B-splines for the proposed scheme. This…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Reservoir simulators utilize numerical techniques to solve the governing equations of fluid flow in porous media and they are essential tool for oil and gas fields development. In practical reservoir simulation, the finite difference method…
In this paper, we consider global strong solutions and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model in R^d, where d=2 and 3. The well-recognized problem of the global existence of smooth solutions for the 2D…
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of…
In this work, new finite difference schemes are presented for dealing with the upper-convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the…
We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is used for spatial discretization, while the backward Euler…
Simulation of fluid flows is crucial for modeling physical phenomena like meteorology, aerodynamics, and biomedicine. Classical numerical solvers often require fine spatiotemporal grids to satisfy stability, consistency, and convergence…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
In this paper, the pressure correctionfinite element method is proposed for the 2D/3D time-dependent thermomicropolarfluid equations. Thefirst-order and second-order backward difference formulas (BDF) are adopted to approximate the time…
The presented research paper illustrates the development of a new methodology to solve 2-dimensional (2D) Navier-Stoke equations, which Pukhnachev proposed through introducing unknown functions in the stream and pressure functions of fluid…
Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral…
In this paper, we propose and analyze an efficient implicit--explicit (IMEX) second order in time backward differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems using the scalar auxiliary variable…
We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex…
This paper deals with a time-split explicit/implicit approach for solving a two-dimensional hydrodynamic flow model with appropriate initial and boundary conditions. The time-split technique is employed to upwind the convection term and to…
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…
We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite…
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related…