The use of curvilinear coordinates is sometimes indicated by the inherent geometry a fluid dynamics problem, but this introduces fictitious forces into momentum equations that spoil strict conservative form. If one willing to work in three dimensions, these can be eliminated solving for rectangular (Cartesian) components on mesh. A thoroughly geometric approach spacetime demonstrates transparen...

The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered. Starting with an exact non-Markovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. ...

An efficient load flow solution technique is required for taking various control and operations decisions. This paper presents an efficient and robust load flow algorithm for application to transmission and distribution networks. In order to face keen competition in market, the coordinated operation between transmission and distribution systems is required. Therefore, the transmission and distr...

The fictitious domain method with H1-penalty for elliptic problems is considered. We propose a new way to derive the sharp error estimates between the solutions of original elliptic problems and their H1-penalty problems. We find our method of analysis is applicable to parabolic problems while retaining the sharpness of the error estimates. We also prove some regularity theorems for H1-penalty ...

We consider the fictitious domain method with H1-penalty for a parabolic problem. First, the sharp error estimate for the H1penalty problem approximating the original problem is derived. Then, we present some regularity analysis and prior estimate to the H1-penalty problem. The finite element approximation is investigated for discrete problems of two types, “continuous-time” and “single-step ba...

The Sub-Mesh Penalty (SMP) method, a new fictitious domain method of high order is presented. The final aim is to develop an efficient coupling between incompressible multiphase flows and fixed or moving obstacles of complex shape. The flow is solved on a fixed Cartesian grid and the solid objects are represented by Lagrangian surface elements. Several validation problems in 2D and 3D are prese...

Control of microstructure parameters that affecting the Al-Ti-C master alloys grain refining efficiency is leading to improve the aluminum grain refinement. This study was an attempt to produce Al-Ti-C master alloys that provide these controlling factors with relying on the solute effect theory. The produced master alloys were examined by using scanning electron microscopy (SEM), energy-dispers...

Augmentation of the SUPS formulation was introduced earlier and successfully applied to solving incompressible NavierStokes equations for both two dimensional and three dimensional problems. Fictitious boundary methods (FBM) is a new methodology that aid the study of flow descriptions around solid obstacles on fixed Cartesian product grids that do not require body confirming meshes. FBM has bee...