Spectral element—Fourier methods for incompressible turbulent flows
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Communication patterns and models in prism: a spectral element-Fourier parallel Navier-Stokes solver
Supercomputing '96 Proceedings of the 1996 ACM/IEEE conference on Supercomputing
An unstructured hp finite-element scheme for fluid flow and heat transfer in moving domains
Journal of Computational Physics
Velocity-Correction Projection Methods for Incompressible Flows
SIAM Journal on Numerical Analysis
De-aliasing on non-uniform grids: algorithms and applications
Journal of Computational Physics
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Space-time discontinuous Galerkin method for nonlinear water waves
Journal of Computational Physics
Discontinuous Galerkin Methods For Solving Elliptic And parabolic Equations: Theory and Implementation
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
Journal of Scientific Computing
The Mortar-Discontinuous Galerkin Method for the 2D Maxwell Eigenproblem
Journal of Scientific Computing
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
Journal of Computational Physics
Journal of Computational Physics
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We present the development of a sliding mesh capability for an unsteady high order (order=3) h/p Discontinuous Galerkin solver for the three-dimensional incompressible Navier-Stokes equations. A high order sliding mesh method is developed and implemented for flow simulation with relative rotational motion of an inner mesh with respect to an outer static mesh, through the use of curved boundary elements and mixed triangular-quadrilateral meshes. A second order stiffly stable method is used to discretise in time the Arbitrary Lagrangian-Eulerian form of the incompressible Navier-Stokes equations. Spatial discretisation is provided by the Symmetric Interior Penalty Galerkin formulation with modal basis functions in the x-y plane, allowing hanging nodes and sliding meshes without the requirement to use mortar type techniques. Spatial discretisation in the z-direction is provided by a purely spectral method that uses Fourier series and allows computation of spanwise periodic three-dimensional flows. The developed solver is shown to provide high order solutions, second order in time convergence rates and spectral convergence when solving the incompressible Navier-Stokes equations on meshes where fixed and rotating elements coexist. In addition, an exact implementation of the no-slip boundary condition is included for curved edges; circular arcs and NACA 4-digit airfoils, where analytic expressions for the geometry are used to compute the required metrics. The solver capabilities are tested for a number of two dimensional problems governed by the incompressible Navier-Stokes equations on static and rotating meshes: the Taylor vortex problem, a static and rotating symmetric NACA0015 airfoil and flows through three bladed cross-flow turbines. In addition, three dimensional flow solutions are demonstrated for a three bladed cross-flow turbine and a circular cylinder shadowed by a pitching NACA0012 airfoil.