A Runge-Kutta Discontinuous-Galerkin Level-Set Method for Unsteady Compressible Two-Fluid Flow

In this work a numerical method for the solution of the two-dimensional Euler equations describing unsteady compressible two-fluid flow is presented. The method is based on the combination of a Runge-Kutta discontinuous Galerkin discretization of the Euler equations and a level-set method for the treatment of the two-fluid interface. The...

A Runge-Kutta Discontinuous-Galerkin Level-Set Method for Unsteady Compressible Two-Fluid Flow

In this work a numerical method for the solution of the two-dimensional Euler equations describing unsteady compressible two-fluid flow is presented. The method is based on the combination of a Runge-Kutta discontinuous Galerkin discretization of the Euler equations and a level-set method for the treatment of the two-fluid interface. The...

A level-set based topology optimization using the element connectivity parameterization method

This contribution presents a novel and versatile approach to geometrically nonlinear topology optimization by combining the level-set method with the element connectivity parameterization method or ECP. The combined advantages of both methods open up the possibility to treat a wide range of optimization problems involving complex physical and/or...

Pushing the Boundaries: Level-set Methods and Geometrical Nonlinearities in Structural Topology Optimization

This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself. Concerning the first topic, we investigate...

Volume-Preserving Continuous Galerkin Level-Set Approach for Linear Finite Elements

Many physical phenomena can be described as the evolution of two phases coexisting within the same domain. Examples of such phenomena are the transport of gas and oil, solidification and phase transformations. Each of these phenomena require a description of the dynamics under which the phases change and a technique for tracking the interface...

Developing a second order accurate level-set method for solving the one-dimensional Stefan problem

This work aims at finding a second order accurate level-set method which solves the Stefan problem with non-homogeneous Dirichlet boundary conditions in one dimension. The numerical accuracy of the FTCS-scheme, BTCS-scheme and Crank-Nicolson scheme for the discretization of the heat equation was considered, as well as the accuracy of the first...