A numerical investigation of directional binary alloy solidification processes is presented. In particular, a mathematical model is developed to study macrosegregation patterns as a consequence of thermal-solutal convection in the melt and mushy zone. A good understanding of the basic mechanisms of macrosegregation is helpful in designing and controlling solidification processes in order to ach...

The current paradigm argues the Moon formed after a giant impact that produced a deep lunar magma ocean (LMO). After a period of turbulent convection, the LMO experienced fractional crystallization, causing the initially peridotitic liquid to evolve to a plagioclase-saturated ferrobasalt. The lunar crust, much of which comprises 93-98% pure anorthosite [1,2], formed by flotation of positively b...

We report the observation of defects with fractional topological charges (disclinations) in square and hexagonal patterns as numerical solutions of several generic equations describing many pattern-forming systems: Swift-Hohenberg equation, damped Kuramoto-Sivashinsky equation, as well as nonlinear evolution equations describing large-scale Rayleigh-Benard and Marangoni convection in systems wi...

This study advances the understanding of how parameterized physical processes affect the development of tropical cyclones (TCs) in the Community Atmosphere Model (CAM) using the Reed–Jablonowski TC test case. It examines the impact of changes in 24 parameters across multiple physical parameterization schemes that represent convection, turbulence, precipitation, and cloud processes. The one-at-a...

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two–phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimizat...

This work investigates how we can extend the invariant subspace method to $$(2+1)$$ -dimensional time-fractional non-linear PDEs. More precisely, systematic study has been provided for constructing various dimensions of subspaces generalized convection–reaction–diffusion wave equation along with initial conditions first time. Additionally, special types above-mentioned are discussed through thi...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

The motivation for this research stems from the high-speed chemical reacting flows which have stiff reaction terms, where the chemical time scales are often much smaller than the fluid dynamics time scales. It is usually too expensive to resolve all the spatial/temporal scales if we are only interested in the main flow. On the other hand, insufficient spatial/temporal resolution will cause the ...