Download or read book A Reconstructed Discontinuous Galerkin Method for the Compressible Navier Stokes Equations on Arbitrary Grids written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.

Download or read book Reconstructed Discontinous Galerkin Method for the Compressible Navier Stokes Equations in Arbitrary Langrangian and Eulerian Formulation written by Chuanjin Wang and published by . This book was released on 2017 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Parallel Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Aritrary Grids written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thus to provide a simple, accurate, consistent, and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations. A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method, which is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model. The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a better performance than the third order DG method, in terms of both computing costs and storage requirements.

Download or read book A Reconstructed Discontinuous Galerkin Method for the Compressible Navier Stokes Equations on Hybrid Grids written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A reconstructed discontinuous Galerkin (rDG(P1P2)) method, originally introduced for the compressible Euler equations, is developed for the solution of the compressible Navier- Stokes equations on 3D hybrid grids. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for the computation of the inviscid fluxes and the viscous fluxes using the second formulation of Bassi and Reay (Bassi-Rebay II). The developed rDG(P1P2) method is used to compute a variety of flow problems to assess its accuracy, efficiency, and robustness. The numerical results demonstrate that the rDG(P1P2) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the large eddy simulation (LES) and direct numerical simulation (DNS) of compressible turbulent flows.

Download or read book Discontinuous Galerkin Method written by Vít Dolejší and published by Springer. This book was released on 2015-07-17 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.

Download or read book Discontinuous Galerkin Methods for the Unsteady Compressible Navier stokes Equations written by Gregor Gassner and published by . This book was released on 2009 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Discontinuous Galerkin Method for the Compressible Navier Stokes Equations in Stationary and Moving 3D Domains written by Igor Lomtev and published by . This book was released on 1999 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Entropy Stable Spacetime Discontinuous Galerkin Method for the Two dimensional Compressible Navier Stokes Equations written by Andreas Hiltebrand and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discontinuous Galerkin Solution of the Navier Stokes Equations on Deformable Domains written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain, By writing the Navier-Stokes 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 Runge-Kutta method, For general domain changes, the standard scheme fails to preserve exactly the free-stream solution which leads to some accuracy degradation, especially for low 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.

Download or read book Frontiers in Physics Rising Stars written by Alex Hansen and published by Frontiers Media SA. This book was released on 2021-10-04 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive High order Methods in Computational Fluid Dynamics written by Z. J. Wang and published by World Scientific. This book was released on 2011 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.

Download or read book Mathematical Reviews written by and published by . This book was released on 2005-06 with total page 1108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Efficiency of Implicit Discontinuous Galerkin Spectral Element Methods for the Unsteady Compressible Navier Stokes Equations written by Serena Vangelatos and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discontinuous Galerkin Methods for the Incompressible Navier stokes Equations written by Daniele Antonio Di Pietro and published by . This book was released on 2006 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Parallel High order Discontinuous Galerkin Solver for the Unsteady Incompressible Navier Stokes Equations in Complex Geometries written by Khosro Shahbazi and published by . This book was released on 2007 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: We verify the accuracy and stability of the method on several two- and three-dimensional benchmarking problems. On the challenging Orr-Sommerfeld test problem, the equal-order polynomial approximation of the velocity and pressure (Pk - Pk) leads to a stable and accurate solution, while the mixed-order method (Pk - Pk-1) yields a non-physical instability. In simulating vortex shedding past a square cylinder at Re = 100 and in simulating a three-dimensional backward-facing step flow using the equal-order method, excellent agreement with other computational and experimental results are obtained. The developed solver is used to study flow through a two-dimensional bileaflet mechanical heart valve geometry. We conclude that the proposed discontinuous Galerkin method with the Pk - Pk formulation is a suitable scheme for simulations of flows through mechanical heart valve geometries. We develop a parallel method and corresponding code for the numerical solution of the unsteady incompressible Navier-Stokes equations, with application to the direct numerical simulation of transitional and turbulent flows through mechanical heart valves. The solver is based on a simple and efficient scheme, namely a high-order discontinuous Galerkin method on triangular and tetrahedral elements. Spatial discretization of the Stokes operator employed both equal-order (Pk - Pk) and mixed-order (Pk - Pk-1) velocity and pressure approximations. The interior penalty method and local Lax-Friedrichs fluxes are used for the discretizations of the viscous term and the nonlinear term in the divergence form, respectively. A second order approximate algebraic splitting is used to decouple the velocity and pressure calculations leading to an algebraic Helmholtz equation for each component of the velocity and a consistent Poisson equation for the pressure. The consistent Poisson operator is replaced by an equivalent operator, namely that arising from the interior penalty discretization of the standard Poisson operator with appropriate boundary conditions. An explicit lower bound is derived for the penalty parameter of the interior penalty method that ensures the coercivity of the bilinear form. Efficiency aspects of the scheme include knowing an explicit expression for the penalty parameter of the interior penalty method and compact stencil size for the discretizations of the velocity and pressure equations and the nonlinear term.

Download or read book An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method written by Shukai Du and published by Springer. This book was released on 2019-09-14 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method.

Download or read book Adaptive multilevel Lagrange Galerkin methods for the incomprressible navier stokes equation written by Achim Schmidt and published by . This book was released on 1998 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: