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Utilization of the Brinkman Penalization to Represent Geometries in a High-Order Discontinuous Galerkin Scheme on Octree Meshes

Nikhil Anand, Neda Ebrahimi Pour, Harald Klimach, Sabine Roller
2019 Symmetry  
We investigate the suitability of the Brinkman penalization method in the context of a high-order discontinuous Galerkin scheme to represent wall boundaries in compressible flow simulations.  ...  We explain the Brinkman penalization method and its application in our open-source implementation of the discontinuous Galerkin scheme, Ateles.  ...  The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  ... 
doi:10.3390/sym11091126 fatcat:bxb2ltjr45f4lgu7cvwhtzcuje

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
The latter would allow better use of parallel computers, since time-stepping is essentially a serial process. Moreover, it would be good for the methods to be of high order accuracy.  ...  Our objective is to simulate transport processes over very long time periods, as needed in, e.g., the simulation of geologic carbon sequestration.  ...  We show how to solve the equations using a global implicit approach in an efficient way, and we present the derived computational results.  ... 
doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  
We develop a hybrid scheme consisting of a combination of a second order MUSCL scheme and a high order finite difference scheme.  ...  The hybrid scheme is constructed in such a way that we can prove that it is stable. We can also show that it is high order accurate in smooth domains and oscillatory free close to the shock.  ...  For time discretization, we apply the fully implicit Crank-Nicolson scheme of 2nd order accuracy while we utilize the high order Q_2 P_1 finite element pair for discretization in space which can be applied  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e

Resolution of Tip Vortices by grid-based, grid-free and coupled methods using CFD

Mahesh Datta Dhone
The work focuses on a hybrid method as a coupling of grid based and grid free vortex method.  ...  The vortex structure resolution is one of the vital problems of CFD as inherent artificial dissipation effects lead to an unphysical strong decay of the vortices.  ...  Nikolai Kornev, you have been a tremendous mentor for me who has continually and persuasively conveyed a spirit of adventure in regard to the thesis work.  ... 
doi:10.18453/rosdok_id00002635 fatcat:tuokvnj3d5dmhd2pfrpoi5vgbq