Amount Of Artificial Dissipation Research Articles

MHD simulations of cool core clusters

AbstractUsing Smoothed Particle Magneto Hydrodynamics (Dolag & Stasyszyn), we study the effects of magnetic fields in galaxy clusters with the aim to infer their dynamical role within the cool core region. Therefore we we investigate the role of regularization as well as divergence cleaning schemes (Stasyszyn & Dolag 2009). We run cosmological simulations of a reference cluster in order to evaluate our various implementation in a realistic scenario. The preliminary results indicate that the final magnetic field profile in the simulations depends only on the amount of artificial dissipation, but not in the amount of numerical div(B) present in the different implementation. We also present first results from simulations which are including radiative cooling and star formation. Even at the this low resolution we find a strong additional amplification of the magnetic field within the cool core region indicating that magnetic pressure could become comparable to the thermal pressure in theses regimes.

An efficient and robust implicit operator for upwind point Gauss–Seidel method

An efficient and robust implicit operator for the point Gauss–Seidel method is presented for solving the compressible Euler equations. The new implicit operator was derived by adding a scalar form of artificial dissipation to the upwind implicit side. The amount of artificial dissipation was locally adjusted using a weighting factor based on the solution gradient. For validation, the performance of the new implicit operator was compared in detail with that of several existing implicit operators which have been widely used for solving the flow equations. Numerical experiments showed that the stability and convergence characteristics of the new implicit operator are significantly better than those of other existing implicit operators for calculating flows ranging from subsonic to hypersonic speeds.

On two-fluid equations for dispersed incompressible two-phase flow

This paper deals with the two-fluid formulation for dispersed two-phase flow. In one space dimension the equations with constant viscosity for both phases are shown to result in a locally in time well-posed periodic problem but without viscosity there are regions in phase space where the problem is non-hyperbolic. It is shown that the viscid problem linearized at constant states in the non-hyperbolic region is terribly unstable for small viscosity coefficients. By numerical experiments for the solution to a model problem it is demonstrated that for smooth initial data in the non-hyperbolic region, discontinuities seem to form. Second order artificial dissipation is added, in an effort to regularize the problem. Numerical examples are given, for different types of initial data. For initial data that is smooth in the non-hyperbolic region, the formation of jumps, or viscid layers, is strongly dependent on the amount of artificial dissipation. No convergence is obtained as the amount of artificial dissipation is diminished. On the other hand, if the initial data is smooth only in the hyperbolic region and with jumps through the non-hyperbolic region, then the jumps or viscid layers that later form, can damp the onset of new layers. In this case convergence in the L2 sense seem to hold, the computed solutions to the regularized problem approach a weak solution as the artificial dissipation is diminished.

Convergence Acceleration for Hyperbolic Systems Using Semicirculant Approximations

The iterative solution of systems of equations arising from systems of hyperbolic, time-independent partial differential equations (PDEs) is studied. The PDEs are discretized using a finite volume or finite difference approximation on a structured grid. A convergence acceleration technique where a semicirculant approximation of the spatial difference operator is employed as preconditioner is considered. The spectrum of the preconditioned coefficient matrix is analyzed for a model problem. It is shown that, asymptotically, the time step for the forward Euler method could be chosen as a constant, which is independent of the number of grid points and the artificial viscosity parameter. By linearizing the Euler equations around an approximate solution, a system of linear PDEs with variable coefficients is formed. When utilizing the semicirculant (SC) preconditioner for this problem, which has properties very similar to the full nonlinear equations, numerical experiments show that the favorable convergence properties hold also here. We compare the results for the SC method to those of a multigrid (MG) scheme. The number of iterations and the arithmetic complexities are considered, and it is clear that the SC method is more efficient for the problems studied. Also, the MG scheme is sensitive to the amount of artificial dissipation added, while the SC method is not.

Assessment of Artificial Dissipation Models for Three-Dimensional Incompressible Flow Solutions

Various approaches for constructing artificial dissipation terms for three-dimensional artificial compressibility algorithms are presented and evaluated. Two, second-order accurate, central-differencing schemes, with explicitly added scalar and matrix-valued fourth-difference artificial dissipation, respectively, and a third-order accurate flux-difference splitting upwind scheme are implemented in a multigrid time-stepping procedure and applied to calculate laminar flow through a strongly curved duct. Extensive grid-refinement studies are carried out to investigate the grid sensitivity of each discretization approach. The calculations indicate that even the finest mesh employed, consisting of over 700,000 grid nodes, is not sufficient to establish grid independent solutions. However, all three schemes appear to converge toward the same solution as the grid spacing approaches zero. The matrix-valued dissipation scheme introduces the least amount of artificial dissipation and should be expected to yield the most accurate solutions on a given mesh. The flux-difference splitting upwind scheme, on the other hand, is more dissipative and, thus, particularly sensitive to grid resolution, but exhibits the best overall convergence characteristics on grids with large aspect ratios.

Computation of Unsteady Viscous Flow Through Turbomachinery Blade Row Due to Upstream Rotor Wakes

A time-accurate, two-dimensional, pressure-based, Navier–Stokes solver for incompressible flow is developed and used to carry out the numerical simulation of rotor–stator interaction. A low-Reynolds-number form of the two-equation turbulence model is used to account for the turbulence effects. In order to improve the accuracy of the numerical scheme, a central differencing plus an artificial dissipation scheme is implemented to provide precise control of numerical dissipation. An inner loop iteration scheme is used at each time step to account for the nonlinear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor–stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake. The predicted unsteady wake profiles are compared with the available experimental data and the agreement is good. The numerical results are interpreted to draw conclusions on the unsteady wake transport mechanism in the blade passage.

Multigrid acceleration of a block structured compressible flow solver

We study a multiblock method for compressible turbulent flow simulations and present results obtained from calculations on a two-element airfoil. A cell-vertex or vertex-based spatial discretization method and explicit multistage Runge-Kutta time stepping are used. The vertex-based method is found to give better results than the cell-vertex method. In the latter method a larger amount of artificial dissipation is required since different control volumes are used for the discretization of the viscous and convective fluxes. The slow convergence of the time stepping method makes a multigrid acceleration technique indispensable. This technique leads to an acceleration by about a factor of 10. The numerical predictions are in good agreement with experimental results. It is shown that the convergence of the multigrid process depends considerably on the ordering of the various loops. If the block loop is put inside the stage loop the process converges more rapidly than if the block loop is situated outside the stage loop in case a three-stage Runge-Kutta method is used. If a five-stage scheme is adopted the process does not converge in the latter block ordering. Finally, the process based on the five-stage scheme is about 60% more efficient than with the three-stage scheme, if the block loop is inside the stage loop.