In this article, we analyze the fractional-step θ method for the time-dependent convectiondiffusion equation. In our implementation, we completely separate the convection operator from the diffusion operator, and stabilize the convective solve using a streamline upwinded PetrovGalerkin (SUPG) method. We establish a priori error estimates and show that optimal values of θ yield a scheme that is ...

Randall, D.A., 1989. Cloud Parameterization for climate modeling: status and prospects. Atmos. Res., 23: 245-361. The current status of cloud parameterization research is reviewed. It is emphasized that the upper tropospheric stratiform clouds associated with deep convection are both physically important and poorly parameterized in current models. Emerging parameterizations are described in gen...

This work proposes a numerical scheme for class of time-fractional convection–reaction–diffusion problems with time lag. Time-fractional derivative is considered in the Caputo sense. The comprises discretization technique given by Crank and Nicolson temporal direction spline functions tension factor are used spatial direction. Through von Neumann stability analysis, shown conditionally stable. ...

Recent physical theories for the formation of the Earth suggest that about 4.5 b.y. ago the mantle of the Earth was partially or completely molten. Fractional crystallization of this hypothetical magma ocean would result in a strong chemical stratification of the Earth's mantle. Such a scenario is controversial from the geochemical point of view. However, it has been noted that the simple scena...

In this paper, the Elzaki transform decomposition method is implemented to solve time-fractional Swift–Hohenberg equations. The presented model related temperature and thermal convection of fluid dynamics, which can also be used explain formation process in liquid surfaces bounded along a horizontally well-conducting boundary. Caputo manner, fractional derivative described. suggested easy imple...

In this article we study the convergence and the error bound for the solution of the convection diffusion reaction equation using overlapping Schwarz wave form relaxation method combined with the first order fractional splitting method (Strang’s splitting) as basic solver. We extended the study to solve decoupled and coupled system of equations of same class in order to demonstrate the effect o...

The probabilistic bulk convection model (PBCM) developed in a companion paper is here extended to shallow nonprecipitating convection. The PBCMunifies the clear-sky and shallow convection boundary layer regimes by obtaining mixed-layer growth, cloud fraction, and convective inhibition from a single parameterization based on physical principles. The evolution of the shallow convection PBCM is ba...

Fourth-order combined compact finite difference scheme is given for solving the time fractional convection–diffusion–reaction equation with variable coefficients. We introduce the flux as a new variable and transform the original equation into a system of two equations. Compact difference is used as a high-order approximation for spatial derivatives of integer order in the coupled partial diffe...

4 This study examines the response of tropical precipitation extremes to warming in organized 5 convection using a cloud-resolving model. Vertical shear is imposed to organize the convec6 tion into squall lines. Earlier studies show that in disorganized convection, the fractional 7 increase of precipitation extremes is similar to that of surface water vapor, which is substan8 tially smaller tha...