We report on recent work on adaptive timestep control for weakly instationary gas flows [16, 18, 17] carried out within SFB 401, TPA3. The method which we implement and extend is a space-time splitting of adjoint error representations for target functionals due to Süli [19] and Hartmann [10]. In this paper, we first review the method for scalar, 1D, conservation laws. We design a test problem f...

The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady flow equations. The objective of the analysis is to compute a complex flow solution that represents the amplitude and phase of the unsteady flow perturbation for the frequency of unsteadiness of interest. The ...

In this article, a time dependent partial differential equation is used to model the nonlinear boundary value problem describing heat transfer through a radial porous moving fin with rectangular profile. The study is performed by applying a numerical solver in MATLAB (pdepe), which is a centered finite difference scheme. The thermal conductivity and fin surface emissivity are linearly ...

This work focuses on the derivation and analysis of a novel, strongly-coupled partitioned method for fluid–structure interaction problems. The flow is assumed to be viscous incompressible, structure modeled using linear elastodynamics equations. We assume that thick, i.e., same number spatial dimensions as fluid. Our newly developed numerical based Robin boundary conditions, well refactorizatio...

The development and applications of a parallel, time-dependent, three-dimensional incompressible Navier-Stokes flow solver and a parallel multigrid elliptic kernel are described. The flow solver is based on a second-order projection method applied to a staggered finite-difference grid. The multigrid algorithms implemented in the parallel elliptic kernel, which is used by the flow solver, are V-...

We describe numerical algorithms and parallel implementations of a time-dependent, incompressible Navier-Stokes flow solver and a multigrid elliptic solver which is also used as a computation kernel in the flow solver. ~’he flow solver is based on a second-order projection method (Bell et. al [2]) applied to a slaggered finite-difference grid. The multigrid elliptic solver uses the full V-cycle...

Stability analysis of the numerical Method of characteristics applied to energy-preserving systems. Abstract We study numerical (in)stability of the Method of characteristics (MoC) applied to a system of non-dissipative hyperbolic partial differential equations (PDEs) with periodic boundary conditions. We consider three different solvers along the characteristics: simple Euler (SE), modified Eu...

In implicit upwind methods for the solution of linearized Euler equations, one of the key issues is to balance large time steps, leading to a fast convergence behavior, and small time steps, needed to sufficiently resolve relevant flow features. A time step is determined by choosing a CourantFriedrichs-Levy (CFL) number in every iteration. A novel CFL evolution strategy is introduced and compar...

Abstract. This paper aims at coupling two known CFD techniques, namely multigrid and parallelization, in an existing Euler equations solver for 2D and 3D unstructured grids. The solver is based on a time-marching formulation for the high-subsonic/transonic flow equations and a pointwise implicit solution algorithm. The gain from the combined use of multigrid and parallelization is the reduction...

The use of an efficient linear solver is very important to reduce the overall runtime of a flow simulation. However, if a linear solver will be very fast e.g. in case of a time dependent model it does not have to be efficient in case of a steady-state model. The efficiency of the linear solver may even change during a simulation run. Hence, there is the need to develop a solver control which ch...