scholarly journals Discontinuous Galerkin method with the spectral deferred correction time-integration scheme and a modified moment limiter for adaptive grids

2012 ◽  
Vol 7 (2) ◽  
pp. 133-174
Author(s):  
Leandro Gryngarten ◽  
Andrew Smith ◽  
Suresh Menon
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Time Integration ◽  
Integration Scheme ◽  
Adaptive Grids ◽  
Deferred Correction ◽  
Time Integration Scheme ◽  
Spectral Deferred Correction

Assessment of a High-Order Discontinuous Galerkin Method for the Direct Numerical Simulation of Transition at Low-Reynolds Number in the T106C High-Lift Low Pressure Turbine Cascade

2014 ◽  
Author(s):  
Koen Hillewaert ◽  
Corentin Carton de Wiart ◽  
Guillaume Verheylewegen ◽  
Tony Arts
Keyword(s):  
Reynolds Number ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Low Reynolds Number ◽  
Time Integration ◽  
High Order ◽  
Implicit Time ◽  
Flow Field Characteristics ◽  
Low Reynolds

An implicit time integration, high-order discontinuous Galerkin method is assessed on the DNS of the flow in the T106C cascade at low Reynolds number. This code, aimed at providing high orders of accuracy on unstructured meshes for DNS and LES simulations on industrial geometries, was previously successfully assessed on fundamental, academic test cases. The computational results are compared to the experimental values and literature, and the obtained flow field characteristics are discussed. Although adequate resolution is supposed to be attained, discrepancies with respect to the experiment are found. These differences were furthermore consistently found by all authors in the workshop on high-order methods for CFD. The origins are therefore conjectured to result from insufficient adequation between computational setup and experiments, as no modeling is assumed. A plan for further investigation is proposed.

Wavelets and adaptive grids for the discontinuous Galerkin method

2005 ◽  
Vol 39 (1-3) ◽  
pp. 143-154 ◽  
Author(s):  
Jorge L. D�az Calle ◽  
Philippe R. B. Devloo ◽  
S�nia M. Gomes
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Adaptive Grids

scholarly journals A Hybrid Time Integration Scheme for the Discontinuous Galerkin Discretizations of Convection-Dominated Problems

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1870
Author(s):  
Liang Li ◽  
Songping Wu
Keyword(s):  
Discontinuous Galerkin ◽  
Time Integration ◽  
Integration Scheme ◽  
Hybrid Scheme ◽  
Time Step ◽  
Third Order ◽  
Element Size ◽  
Time Integration Scheme ◽  
Dg Method ◽  
Convection Dominated

Discontinuous Galerkin (DG) method is a popular high-order accurate method for solving unsteady convection-dominated problems. After spatially discretizing the problem with the DG method, a time integration scheme is necessary for evolving the result. Owing to the stability-based restriction, the time step for an explicit scheme is limited by the smallest element size within the mesh, making the calculation inefficient. In this paper, a hybrid scheme comprising a three-stage, third-order accurate, and strong stability preserving Runge–Kutta (SSP-RK3) scheme and the three-stage, third-order accurate, L-stable, and diagonally implicit Runge–Kutta (LDIRK3) scheme is proposed. By dealing with the coarse and the refined elements with the explicit and implicit schemes, respectively, the time step for the hybrid scheme is free from the limitation of the smallest element size, making the simulation much more efficient. Numerical tests and comparison studies were made to show the performance of the hybrid scheme.

scholarly journals Penyelesaian Numerik Persamaan Advection Dengan Radial Point Interpolation Method dan Integrasi Waktu Dengan Discontinuous Galerkin Method

Teknik ◽  
2016 ◽  
Vol 37 (2) ◽  
pp. 64
Author(s):  
Kresno Wikan Sadono
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Interpolation Method ◽  
Time Integration ◽  
Advection Equation ◽  
Time Increment ◽  
Radial Basis ◽  
Point Interpolation Method ◽  
Point Interpolation

Persamaan differensial banyak digunakan untuk menggambarkan berbagai fenomena dalam bidang sains dan rekayasa. Berbagai masalah komplek dalam kehidupan sehari-hari dapat dimodelkan dengan persamaan differensial dan diselesaikan dengan metode numerik. Salah satu metode numerik, yaitu metode meshfree atau meshless berkembang akhir-akhir ini, tanpa proses pembuatan elemen pada domain. Penelitian ini menggabungkan metode meshless yaitu radial basis point interpolation method (RPIM) dengan integrasi waktu discontinuous Galerkin method (DGM), metode ini disebut RPIM-DGM. Metode RPIM-DGM diaplikasikan pada advection equation pada satu dimensi. RPIM menggunakan basis function multiquadratic function (MQ) dan integrasi waktu diturunkan untuk linear-DGM maupun quadratic-DGM. Hasil simulasi menunjukkan, metode ini mendekati hasil analitis dengan baik. Hasil simulasi numerik dengan RPIM DGM menunjukkan semakin banyak node dan semakin kecil time increment menunjukkan hasil numerik semakin akurat. Hasil lain menunjukkan, integrasi numerik dengan quadratic-DGM untuk suatu time increment dan jumlah node tertentu semakin meningkatkan akurasi dibandingkan dengan linear-DGM. [Title: Numerical solution of advection equation with radial basis interpolation method and discontinuous Galerkin method for time integration] Differential equation is widely used to describe a variety of phenomena in science and engineering. A variety of complex issues in everyday life can be modeled with differential equations and solved by numerical method. One of the numerical methods, the method meshfree or meshless developing lately, without making use of the elements in the domain. The research combines methods meshless, i.e. radial basis point interpolation method with discontinuous Galerkin method as time integration method. This method is called RPIM-DGM. The RPIM-DGM applied to one dimension advection equation. The RPIM using basis function multiquadratic function and time integration is derived for linear-DGM and quadratic-DGM. The simulation result shows that this numerical method, close to the results exact well. The results of numerical simulations with RPIM-DGM show, the more nodes and the smaller the time increment, the more accurate the numerical results. Other results showed, integration with quadratic-DGM for a time increment, and a certain number of nodes, further improving accuracy, compared with the linear-DGM. 

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