Journal of Scientific Computing
Spectral methods on triangles and other domains
Journal of Scientific Computing
An analysis of the fractional step method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex
SIAM Journal on Numerical Analysis
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Stable Spectral Methods on Tetrahedral Elements
SIAM Journal on Scientific Computing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Algebraic splitting for incompressible Navier-Stokes equations
Journal of Computational Physics
Performance of Discontinuous Galerkin Methods for Elliptic PDEs
SIAM Journal on Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Local Discontinuous Galerkin Methods for the Stokes System
SIAM Journal on Numerical Analysis
Mixed hp-DGFEM for Incompressible Flows
SIAM Journal on Numerical Analysis
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Short Note: An explicit expression for the penalty parameter of the interior penalty method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
An Entropy Adjoint Approach to Mesh Refinement
SIAM Journal on Scientific Computing
Semi-Lagrangian multistep exponential integrators for index 2 differential-algebraic systems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
A SIMPLE based discontinuous Galerkin solver for steady incompressible flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.51 |
We present a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations in convection-dominated flows using triangular and tetrahedral meshes. The scheme is based on a semi-explicit temporal discretization with explicit treatment of the nonlinear term and implicit treatment of the Stokes operator. The nonlinear term is discretized in divergence form by using the local Lax-Friedrichs fluxes; thus, local conservativity is inherent. Spatial discretization of the Stokes operator has employed both equal-order (P"k-P"k) and mixed-order (P"k-P"k"-"1) velocity and pressure approximations. 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 (in stability and convergence) operator, namely that arising from the interior penalty discretization of the standard Poisson operator with appropriate boundary conditions. This yields a simpler and more efficient method, characterized by a compact stencil size. We show the temporal and spatial behavior of the method by solving some popular benchmarking tests. For an unsteady Stokes problem, second-order temporal convergence is obtained, while for the Taylor vortex test problem on both semi-structured and fully unstructured triangular meshes, spectral convergence with respect to the polynomial degree k is obtained. By studying the Orr-Sommerfeld stability problem, we demonstrate that the P"k-P"k method yields a stable solution, while the P"k-P"k"-"1 formulation leads to unphysical instability. The good performance of the method is further shown by simulating vortex shedding in flow past a square cylinder. We conclude that the proposed discontinuous Galerkin method with the P"k-P"k formulation is an efficient scheme for accurate and stable solution of the unsteady Navier-Stokes equations in convection-dominated flows.