For Stokes equations with a discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, it is known that the pressure is discontinuous and the velocity is non-smooth. It has been shown that these discontinuities are coupled together, which makes it difficult to obtain accurate numerical solutions. In this paper, a new numerical method that decouples the jum...

This paper presents a systematic control inputs optimization method for melting interface tracking in laser-aided powder deposition (LAPD) processes. Using a proposed interface approximation and a coordinate system moving with the laser source, and adopting the enhanced thermal conductivity method, the process model is first reduced to a set of coupled partial differential equations (PDEs) in f...

[Received 8 May 1987 and in revised form 23 May 1988] In this paper the two-dimensional flow of fresh and salt water through a homogeneous aquifer is considered. The two fluids are assumed to be separated by a sharp interface. They differ only in their specific weight. This difference induces a flow in the aquifer which in turn causes a motion of the interface. We present a mathematical formula...

For Stokes equations with discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, the pressure is known to be discontinuous and the velocity is known to be non-smooth. It has been shown that these discontinuities are coupled together which makes it difficult to obtain accurate numerical solutions. In this paper, a second order accurate numerical method ...

Phaseeld models are attractive for numerical simulation of solidi cation. The derivation ensures that moving boundaries in the sharp interface formulation are replaced by thin regions of width given implicitly by the solution. The need to explicitly track the location of geometrically complex solid-liquid interfaces is eliminated. The sharp interface problem is formally recovered as the di use ...

This article proposes a new approach for centralized path planning of multiple aircraft in presence of the obstacle-laden environment under low flying rules. The problem considers as a unified nonlinear constraint optimization problem. The minimum time and control investigate as the cost functions and the maximum velocity and power consider as the constraints. The pseudospectral method applies ...