Related papers: Solution of a Scalar Convection-Diffusion Equation…
A framework of finite-velocity model based Boltzmann equation has been developed for convection-diffusion equations. These velocities are kept flexible and adjusted to control numerical diffusion. A flux difference splitting based kinetic…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
We study a three-dimensional rapidly rotating convection model featuring tall columnar structures, in the absence of thermal diffusion. We establish the global existence and uniqueness of weak solutions, as well as the Hadamard…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
The equation governing the streaming of a quantity down its gradient superficially looks similar to the simple constant velocity advection equation. In fact, it is the same as an advection equation if there are no local extrema in the…
On Bakhvalov-type mesh, uniform convergence analysis of finite element method for a 2-D singularly perturbed convection-diffusion problem with exponential layers is still an open problem. Previous attempts have been unsuccessful. The…
In the present article an endeavor is made to solve the variable order fractional diffusion equations using a powerful method viz., Homotopy Analysis method. It is demonstrated how the method can be used while solving approximately two…
A finite element method of any order is applied on a Bakhvalov-type mesh to solve a singularly perturbed convection--diffusion equation in 2D, whose solution exhibits exponential boundary layers. A uniform convergence of (almost) optimal…
Isogeometric analysis was applied very successfully to many problem classes like linear elasticity, heat transfer and incompressible flow problems but its application to compressible flows is very rare. However, its ability to accurately…
Many steady-state transport problems in condensed matter physics can be reduced to a set of coupled diffusion equations. This is true in particular when relaxation processes are sufficiently fast that the system is in the diffusive…
In this paper, we develop a modified nonlinear dynamic diffusion (DD) finite element method for convection-diffusion-reaction equations. This method is free of stabilization parameters and is capable of precluding spurious oscillations. We…
Based on recent developments in physics-informed deep learning and deep hidden physics models, we put forth a framework for discovering turbulence models from scattered and potentially noisy spatio-temporal measurements of the probability…
We explore the applicability of MATLAB for 3D computational fluid dynamics (CFD) of shear-driven indoor airflows. A new scale-resolving, large-eddy simulation (LES) solver titled DNSLABIB is proposed for MATLAB utilizing graphics processing…
This paper presents a novel method for solving the 2D advection-diffusion equation using fixed-depth symbolic regression and symbolic differentiation without expression trees. The method is applied to two cases with distinct initial and…
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…
Superluminal propagation is an intrinsic problem in the diffusion equation and has not been effectively addressed for a long time. In this work, a rigorous solution to this issue is obtained under the assumption that particles undergo a…
The Calder\'on problem consists in recovering an unknown coefficient of a partial differential equation from boundary measurements of its solution. These measurements give rise to a highly nonlinear forward operator. As a consequence, the…
In the presented paper known (up to the beginning of 2008) Lie- and non-Lie exact solutions of different $(1+1)$-dimensional diffusion-convection equations of form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$ are collected.
In this article, we propose a novel scalar-transport model for the simulation of scalar quantities in two-phase flows with a phase-field method (diffuse-interface method). In a two-phase flow, the scalar quantities typically have disparate…
In this article we investigate the solution of the steady-state fractional diffusion equation on a bounded domain in $\real^{1}$. From an analysis of the underlying model problem, we postulate that the fractional diffusion operator in the…