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37
Spacetime discontinuous galerkin method for wetchemical etching of microstructures
 Proceedings of European Congress in Applied Sciences and Engineering (ECCOMAS
, 2006
"... Tankers moored at an oil production center. University of Twente Numerical Analysis and Computational Mechanics Group 2 ..."
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Cited by 23 (7 self)
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Tankers moored at an oil production center. University of Twente Numerical Analysis and Computational Mechanics Group 2
Discontinuous Galerkin Solution of the NavierStokes Equations on Deformable Domains
"... We describe a method for computing timedependent solutions to the compressible NavierStokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain. By writing the NavierStokes equations as a conservation law for the ..."
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Cited by 19 (7 self)
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We describe a method for computing timedependent solutions to the compressible NavierStokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain. By writing the NavierStokes equations as a conservation law for the independent variables in the reference configuration, the complexity introduced by variable geometry is reduced to solving a transformed conservation law in a fixed reference configuration. The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, while the time integration is performed using an explicit RungeKutta method. For general domain changes, the standard scheme fails to preserve exactly the freestream solution which leads to a significant accuracy degradation even for high order approximations. This situation is remedied by adding an additional equation for the time evolution of the transformation Jacobian to the original conservation law and correcting for the accumulated metric integration errors. A number of results are shown to illustrate the flexibility of the approach to handle high order approximations on complex geometries.
2008: A discontinuous Galerkin finite element model for morphological evolution under shallow flows
"... We present a discontinuous Galerkin finite element method for two depthaveraged twophase flow models. One of these models contains nonconservative products for which we developed a discontinuous Galerkin finite element formulation in Rhebergen et al. (2008) J. Comput. Phys. 227, 18871922. The ot ..."
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We present a discontinuous Galerkin finite element method for two depthaveraged twophase flow models. One of these models contains nonconservative products for which we developed a discontinuous Galerkin finite element formulation in Rhebergen et al. (2008) J. Comput. Phys. 227, 18871922. The other model is a new depthaveraged twophase flow model we introduce for shallow twophase flows that does not contain nonconservative products. We will compare numerical results of both models and qualitatively validate the models against a laboratory experiment. Furthermore, because of spurious oscillations that may occur near discontinuities, a WENO slope limiter is applied in conjunction with a discontinuity detector to detect regions where spurious oscillations appear. Key words: discontinuous Galerkin finite element methods, multiphase flows, nonconservative products, slope limiter, discontinuity detector
A spacetime discontinuous Galerkin finite element method for twofluid problems
 Journal of Computational Physics
, 2006
"... A spacetime discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cutcell methods the interface between two fluids is tracked in spacetime. The movement of the interface in spacetime is calculated by solving the level set e ..."
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Cited by 3 (2 self)
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A spacetime discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cutcell methods the interface between two fluids is tracked in spacetime. The movement of the interface in spacetime is calculated by solving the level set equation, where the interface geometry is identified with the 0level 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 0level 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: cutcell method, discontinuous Galerkin finite element method, interface tracking, level set method, spacetime, two fluid flows. 1
Very High Order PNPM Schemes on Unstructured Meshes for the Resistive Relativistic MHD Equations
, 903
"... In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space dimensions. The nonlinear system under consideration is purely hyperb ..."
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In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space dimensions. The nonlinear system under consideration is purely hyperbolic and contains a source term, the one for the evolution of the electric field, that becomes stiff for low values of the resistivity. For the spatial discretization we propose to use high order PNPM schemes as introduced in [10] for hyperbolic conservation laws and a high order accurate unsplit time discretization is achieved using the elementlocal spacetime discontinuous Galerkin approach proposed in [11] for onedimensional balance laws with stiff source terms. The divergence free character of the magnetic field is accounted for through the divergence cleaning procedure of Dedner et al. [7]. To validate our high order method we first solve some numerical test cases for which exact analytical reference solutions are known and we also show numerical convergence studies in the stiff limit of the RRMHD equations using PNPM schemes
Advances in Bringing Highorder Methods to Practical Applications in Computational Fluid Dynamics
, 2011
"... This article surveys recent developments in the design and analysis of high order discretization methods for unstructured meshes, with an emphasis on Huynh’s flux reconstruction method, and energy stability. The article also highlights some open issues with respect to energy stability for nonlinear ..."
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Cited by 2 (1 self)
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This article surveys recent developments in the design and analysis of high order discretization methods for unstructured meshes, with an emphasis on Huynh’s flux reconstruction method, and energy stability. The article also highlights some open issues with respect to energy stability for nonlinear problems, and methods for timeintegration. Some representative results of simulations of transitional and turbulent flows are included to illustrate the current state of the art. I.
Explicit Finite Volume Schemes of Arbitrary High Order of Accuracy for Hyperbolic Systems with Stiff Source Terms
, 2007
"... In this article we propose a new class of finite volume schemes of arbitrary accuracy in space and time for systems of hyperbolic balance laws with stiff source terms. The new class of schemes is based on a three stage procedure. First, in order to achieve high order accuracy in space, a nonlinear w ..."
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In this article we propose a new class of finite volume schemes of arbitrary accuracy in space and time for systems of hyperbolic balance laws with stiff source terms. The new class of schemes is based on a three stage procedure. First, in order to achieve high order accuracy in space, a nonlinear weighted essentially nonoscillatory reconstruction procedure is applied to the cell averages at the current time level. Second, the temporal evolution of the resulting reconstruction polynomials is computed locally inside each cell exploiting directly the full system of governing equations. In previous ADER schemes, this was achieved via the CauchyKovalewski procedure, where the governing equation is repeatedly differentiated with respect to space and time to construct a Taylor series expansion of the local solution. As the CauchyKovalewski procedure is based on Taylor series expansions, it is not able to handle systems with stiff source terms since the Taylor series diverges for this case. Therefore, in this article, we present a new strategy that replaces the CauchyKovalewski procedure for high order time interpolation: we present a special local spacetime
Arbitrary Lagrangian Eulerian method
"... A cell by cell anisotropic adaptive mesh ..."
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