A robust mesh optimisation method is presented that directly enforces the resulting deformation to be orientation preserving. Motivated by aspects from mathematical elasticity, the energy functional of the mesh deformation can be related to a stored energy functional of a hyperelastic material. Formulating the functional in the principal invariants of the deformation gradient allows fine grained control over the resulting deformation. Solution techniques for the arising nonconvex and highl...

The aim of this paper is to present a boundary-layer analysis of two-phase dusty non-Newtonian fluid flow along a vertical surface by using a modified power-law viscosity model. This investigation particularly reports the flow behavior of spherical particles suspended in the non-Newtonian fluid. The governing equations are transformed into nonconserved form and then solved straightforwardly by implicit finite difference method. The numerical results of rate of heat transfer, rate of shea...

A viscous damage model including two damage variables - a local and a nonlocal one - coupled through a penalty term is investigated on three different levels: unique solvability, behaviour as the penalization parameter approaches ∞ and optimal control. Existence, uniqueness and regularity of the solutions are proven. In particular, we give an improved result regarding spacial regularity of the nonlocal damage. Lipschitz continuity as well as Fréchet-differentiability of the solution operato...

In this article, we present a-posteriori error estimations in context of optimal control of contact problems; in particular of Signorini’s problem. Due to the contact side-condition, the solution operator of the underlying variational inequality is not differentiable, yet we want to apply Newton’s method. Therefore, the non-smooth problem is regularized by penalization and afterwards discretized by finite elements. We derive optimality systems for the regularized formulation in the continuous...

In this paper, numerical solutions to thermally radiating Marangoni convection of dusty fluid flow along a vertical wavy surface are established. The results are obtained with the understanding that the dust particles are of uniform size and dispersed in optically thick fluid. The numerical solutions of the dimensionless transformed equations are obtained through straightforward implicit finite difference scheme. In order to analyze the influence of various controlling parameters, results are...

We present a new approach to enforcing local maximum principles in finite element schemes for the compressible Euler equations. In contrast to synchronized limiting techniques for systems of conservation laws, the density, momentum, and total energy are constrained in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum are adjusted to incorporate the irreversible effect of density cha...

This paper is concerned with the state-constrained optimal control of the threedimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system as well as existence of optimal solutions, admitting global-in-time solutions, to the optimization problem were shown in the the companion ...

In this thesis we propose a coordinate ascent method for a class of semidefinite programming problems arising in the reformulation of non-convex quadratic optimization problems where the variables are restricted to subsets of the integer numbers. It is known that non-convex quadratic integer problems are NP-hard for two reasons: the non-convexity of the objective function and the restrictions of integrality on the variables. Therefore no polynomial time algorithm is known for solving this cl...

The aim of present paper is to establish the detailed numerical results for bioconvection boundary-layer flow of two-phase dusty nanofluid. The dusty fluid contains gyrotactic microorganisms along an isothermally heated vertical wall. The physical mechanisms responsible for the slip velocity between the dusty fluid and nanoparticles, such as thermophoresis and Brownian motion, are included in this study. The influence of the dusty nanofluid on heat transfer and flow characteristics are i...

This paper addresses the problem of determining cost-minimal process designs for ideal multi-component distillation columns. The special case of binary distillation was considered in former work. Therein, a problem-specific bound-tightening strategy based on monotonic mole fraction profiles of single components was developed to solve the corresponding MINLPs, globally. In the multi-component setting, the mole fraction profiles of single components may not be monotonic, which is why the bound-...

In this paper numerical solutions of a two-phase natural convection dusty fluid flow are presented. The two-phase particulate suspension is investigated along a vertical cone by keeping variable viscosity and thermal conductivity of the carrier phase. Comprehensive flow formations of the gas and particle phases are given with the aim to predict the behavior of heat transport across the heated cone. The influence of i) air with particles, water with particles and oil with particles are shown o...

We present a unique approach for integrating research in High Performance Computing (HPC) as well as photovoltaic (PV) solar farming and battery technologies into a container-based compute center designed for a maximum of energy efficiency, performance and extensibility/scalability. We use NVIDIA Jetson TK1 boards to build a considerably dimensioned cluster of 60 low-power GPUs, attach a 7:5 kWp solar farm and a 8 kWh Lithium-Ion battery power supply and integrate everything into a single-co...

This paper presents a new approach to constraining the eigenvalue range of symmetric tensors in numerical advection schemes based on the flux-corrected transport (FCT) algorithm and a continuous finite element discretization. In the context of element-based FEM-FCT schemes for scalar conservation laws, the numerical solution is evolved using local extremum diminishing (LED) antidi usive corrections of a low order approximation which is assumed to satisfy the relevant inequality constraint...

In this work, various aspects of PDE-based mesh optimisation are treated. Different existing methods are presented, with the focus on a class of nonlinear mesh quality functionals that can guarantee the orientation preserving property. This class is extended from simplex to hypercube meshes in 2d and 3d. The robustness of the resulting mesh optimisation method allows the incorporation of unilateral boundary conditions of place and r-adaptivity with direct control over the resulting cell size...

The paper considers the inuence of thermal Maragoni convection on boundary layer flow of two-phase dusty fluid along a vertical wavy surface. The dimensionless boundary layer equations for two-phase problem are reduced to a convenient form by primitive variable transformation (PVF) and then integrated numerically by employing the implicit finite difference method along with the Thomas Algorithm. The effect of thermal Maragoni convection, dusty water and sinusoidal waveform are discussed in d...

This article is concerned with the class of solutions of gas boundary layer containing uniform, spherical solid particles over the surface of rotating axi-symmetric roundnosed body. By using the method of transformed coordinates, the boundary-layer equations for two-phase flow are mapped into a regular and stationary computational domain and then solved numerically by using implicit finite difference method. In this study, a rotating hemisphere is used as a particular example to elucidat...

The intent of this paper is to establish the detailed parametric study for laminar natural convection ow along a vertical wavy plate. Typical sinusoidal surface is used to elu- cidate the heat transport phenomena for the gas having variable thermophysical properties. From the present analysis, we will interrogate whether the presence of roughness element disturbs the gas ow and alter the physical characteristics associates with the wavy surface or not? The numerical solutions are obt...

The purpose of the present study is to establish the detailed parametric solutions for laminar natural convection flow of two-phase dusty fluid moving along a vertical wavy plate. Typical sinusoidal surface is used to elucidate the heat transport phenomena for the carrier gas having variable thermophysical properties. The governing equations are cast into a system of parabolic partial differential equations by using set of continuous transformations and then the resulting system is integ...

Process intensification of engineering applications in the framework of reacting flows in micromixer devices attracts the attention of engineers and scientists from various fields. With the steadily increasing available computational resources the traditional experimentally supported investigations may be extended by computational ones. For this purpose, a simulation framework based on state of the art numerical techniques extended with special grid deformation techniques has been develo...