Eberhard B

Bio: Eberhard B is an academic researcher. The author has contributed to research in topics: Finite element method & Phase transition. The author has an hindex of 1, co-authored 1 publications receiving 2 citations.

An ALE FEM for solid-liquid phase transitions with free melt surface

Abstract: A finite element method is introduced which is capable to simulate the melting of solid material with a free melt surface. Especially in a micro scale situation, the free capillary surface and its interplay with the solid-liquid interface play an important role. The method is applied to the engineering process of melting the tip of a thin steel wire by laser heating. The mathematical system comprises heat conduction, radiative boundary conditions, and solid-liquid phase transition as well as the fluid dynamics in the liquid region and a free capillary surface. A sharp interface mesh–moving method (complemented by occasional remeshing) is used to track the liquid/solid interface as well as the capillary free boundary.

3D Finite element simulation of a material accumulation process including phase transitions and a capillary surface

Abstract: In this article, the modeling and simulation of a material accumulation process in micro-range based on laser-based free form heading is discussed. The process represents the first step of a material accumulation process which has been developed within the SFB 747 and is modeled mathematically by coupling the Stefan problem with the Navier-Stokes equations including a free capillary surface. For the numerical simulation of the process, two different approaches for handling solid-liquid phase transitions are combined and implemented in a finite element method.

Optimal Control of a Stefan Problem Fully Coupled with Incompressible Navier-Stokes-Equations and Mesh Movement

Abstract: Abstract The optimal control of moving boundary problems receives growing attention in science and technology. We consider the so called two-phase Stefan problem that models a solid and a liquid phase separated by a moving interface. The Stefan problem is coupled with incompressible Navier{Stokes equations. We take a sharp interface model approach and define a quadratic tracking-type cost functional that penalizes the deviation of the interface from the desired state and the control costs. With the formal Lagrange approach and an adjoint system we derive the gradient of the cost functional. The derived formulations can be used to achieve a desired interface position. Among others, we address how to handle the weak discontinuity of the temperature along the interface with mesh movement methods in a finite element framework.

Riccati-feedback Control of a Two-dimensional Two-phase Stefan Problem

Abstract: : We discuss the feedback control problem for a two-dimensional two-phase Stefan problem. In our approach, we use a sharp interface representation in combination with mesh-movement to track the interface position. To attain a feedback control, we apply the linear-quadratic regulator approach to a suitable linearization of the problem. We address details regarding the discretization and the interface representation therein. Further, we document the matrix assembly to generate a non-autonomous generalized differential Riccati equation. To numerically solve the Riccati equation, we use low-rank factored and matrix-valued versions of the non-autonomous backward differentiation formulas, which incorporate implicit index reduction techniques. For the numerical simulation of the feedback controlled Stefan problem, we use a time-adaptive fractional-step-theta scheme. We provide the implementations for the developed methods and test these in several numerical experiments. With these experiments we show that our feedback control approach is applicable to the Stefan control problem and makes this large-scale problem computable. Also, we discuss the influence of several controller design parameters, such as the choice of inputs and outputs.