Tankers moored at an oil production center. University of Twente- Numerical Analysis and Computational Mechanics Group 2

A space-time discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cut-cell methods the interface between two fluids is tracked in space-time. The movement of the interface in space-time is calculated by solving the level set equation, where the interface geometry is identified with the 0-level set. To enhance the accuracy of the interface approximation the level set function is advected with the interface velocity, which for this purpose is extended into the domain. Close to the interface the mesh is locally refined in such a way that the 0-level set coincides with a set of faces in the mesh. The two fluid flow equations are solved on this refined mesh. The procedure is repeated until both the mesh and the flow solution have converged to a reasonable accuracy. The method is tested on linear advection and Euler shock tube problems involving ideal gas and compressible bubbly magma. Oscillations around the interface are eliminated by choosing a suitable interface flux. Key words: cut-cell method, discontinuous Galerkin finite element method, interface tracking, level set method, space-time, two fluid flows. 1

Abstract. Computational Fluid Dynamics is a key enabler for meeting the strategic goals of future air transportation. However, the limitations of today’s numerical tools reduce the scope of innovation in aircraft development, keeping aircraft design at a conservative level. Within the 3 rd Call of the 6 th European Research Framework Programme, the strategic target research project ADIGMA has been initiated. The goal of ADIGMA is the development and utilization of innovative adaptive higher-order methods for the compressible flow equations enabling reliable, mesh independent numerical solutions for large-scale aerodynamic applications in aircraft design. A critical assessment of the newly developed methods for industrial aerodynamic applications will allow the identification of the best numerical strategies for integration as major building blocks for the next generation of industrial flow solvers. In order to meet the ambitious objectives, a partnership of 22 organizations from universities, research organizations and aerospace industry from 10 countries with well proven expertise in CFD has been set up guaranteeing high level research work with a clear path to industrial exploitation. This paper gives on overview of the goals and the planned activities of the 3-years project. 1

Towards affordable CFD simulations of rotors in forward flight

Slip flow boundary conditions in discontinuous

Flow simulation using a boundary conforming discontinuous Galerkin finite element approach for the operational loads survey helicopter rotor in forward flight O.J. Boelens, H. van der Ven, B. Oskam and A.A. HassanNationaal Lucht- en Ruimtevaartlaboratorium National Aerospace Laboratory NLR

Abstract. We deal with a numerical simulation of viscous compressible flows described by the system of the Navier-Stokes equations. We presented a numerical scheme which is based on a discontinuous Galerkin finite element method for a space semi-discretization and the resulting system of ordinary differential equations is discretized by a suitable Predictor-Corrector formula. One numerical example is presented.

Abstract. This paper deals with the numerical solution of a scalar nonlinear convection–diffusion equation. The space semi–discretization is carried out by the discontinuous Galerkin finite element method. Several possibilities of the time discretizations are discussed. To obtain a stable and efficient schemes we use implicit scheme for linear terms in combination with suitable explicit scheme for nonlinear terms, which leads to the necessity to solve only linear problem at each time level.

The numerical method for two fluid flow computations presented in Sollie, Bokhove & van der Vegt, Two Fluid Space-Time Discontinuous Galerkin Finite Element Method. Part I: Numerical Algorithm is applied to a number of one and two dimensional single and two fluid test problems, including a magma- ideal gas shocktube and a helium cylinder- shock wave interaction problem. Keywords: cut-cell, space-time discontinuous Galerkin, front tracking, level set, two fluid flow. 1.

A novel numerical method for two fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local hp-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative. Keywords: cut-cell, space-time discontinuous Galerkin, front tracking, level set, two