Temporal adaptive Euler/Navier-Stokes algorithm involving unstructured dynamic meshes

Abstract

A temporal adaptive algorithm for the time integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal-adaptive algorithm is a time-accurate integration procedure that allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.

Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws

“…These flow features compare favorably with experimental and numerical results of Nagamatsu et al [30]. The superior numerical properties of the LRM [26] allowed the same solution to be computed with greater accuracy using only 8 mesh enrichments, as opposed to the 61 needed with a global time step. A time sequence showing the solution obtained with the LRM on the left and the corresponding partitionings using OCTPART on the right is given in Fig.…”

“…Since flux calculations are typically the most expensive part of the integration, this savings outweighs any possible losses due to using reduced time steps. Choosing time steps that are fractional powers of two also helps to organize the computation [26].…”

“…In order to increase efficiency, temporal adaptivity has been applied to overlapping two-dimensional uniform [3,5,7,15] and unstructured [26] meshes. In Section 3, we introduce an explicit local refinement method (LRM) for the solution of time-dependent conservation laws on three-dimensional unstructured meshes.…”

Implicit Method for the Computation of Unsteady Flows on Unstructured Grids

“…A time-accurate residual averaging formulation [19,43], and temporal adaptation techniques [14], which An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference ap-enable different cells to take a varying number of local proximation for the time derivative, the resulting nonlinear system time steps to get to a particular time level, can be used of equations is solved at each time step by using an agglomeration to realize modest improvements in the performance of multigrid procedure.…”

Time accurate local time stepping for the unsteady shallow water equations

“…Unlike the previous approach, Kleb et al [22] presented a local time stepping technique that was based upon advancing individual cells to a level near that allowed by the CFL limit, which is in essence much more of a local time stepping strategy. Linear interpolation was then used at the interface regions between cells at di erent levels to extract the information at the correct point in time.…”