Discontinuous Galerkin solution of compressible flow in time-dependent domains

2010 ◽  
Vol 80 (8) ◽  
pp. 1612-1623 ◽  
Author(s):  
M. Feistauer ◽  
V. Kučera ◽  
J. Prokopová
Keyword(s):  
Compressible Flow ◽  
Discontinuous Galerkin ◽  
Time Dependent ◽  
Galerkin Solution

Compressible Flow Simulations on a Massively Parallel Computer

1991 ◽  
Vol 02 (01) ◽  
pp. 430-436
Author(s):  
ELAINE S. ORAN ◽  
JAY P. BORIS
Keyword(s):  
Compressible Flow ◽  
Chemical Reactions ◽  
Large Scale ◽  
Model Development ◽  
Time Dependent ◽  
Parallel Computer ◽  
Massively Parallel ◽  
Parallel Solution ◽  
Flow Simulations ◽  
Connection Machine

This paper describes model development and computations of multidimensional, highly compressible, time-dependent reacting on a Connection Machine (CM). We briefly discuss computational timings compared to a Cray YMP speed, optimal use of the hardware and software available, treatment of boundary conditions, and parallel solution of terms representing chemical reactions. In addition, we show the practical use of the system for large-scale reacting and nonreacting flows.

scholarly journals Discontinuous Galerkin time discretization methods for parabolic problems with linear constraints

2019 ◽  
Vol 27 (3) ◽  
pp. 155-182 ◽  
Author(s):  
Igor Voulis ◽  
Arnold Reusken
Keyword(s):  
Discontinuous Galerkin ◽  
Error Bounds ◽  
Convergence Rates ◽  
Time Discretization ◽  
Linear Constraints ◽  
Dirichlet Boundary Conditions ◽  
Time Dependent ◽  
Parabolic Problems ◽  
Discretization Methods ◽  
Optimal Convergence

Abstract We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time-dependent) Dirichlet boundary conditions and the time-dependent Stokes equation with an inhomogeneous divergence constraint. Two common ways of treating such linear constraints, namely explicit or implicit (via Lagrange multipliers) are studied. These different treatments lead to different variational formulations of the parabolic problem. For these formulations we introduce a modification of the standard discontinuous Galerkin (DG) time discretization method in which an appropriate projection is used in the discretization of the constraint. For these discretizations (optimal) error bounds, including superconvergence results, are derived. Discretization error bounds for the Lagrange multiplier are presented. Results of experiments confirm the theoretically predicted optimal convergence rates and show that without the modification the (standard) DG method has sub-optimal convergence behavior.

Discontinuous Galerkin solution of the RANS and kL−k−log(ω) equations for natural and bypass transition

2021 ◽  
Vol 214 ◽  
pp. 104767
Author(s):  
M. Lorini ◽  
F. Bassi ◽  
A. Colombo ◽  
A. Ghidoni ◽  
G. Noventa
Keyword(s):  
Discontinuous Galerkin ◽  
Bypass Transition ◽  
Galerkin Solution
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