No abstract

The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods. The hybrid method of combining high resolution flux with more dissipative solver is an attractive attempt to cure this kind of non-physical phenomenon. In this paper, a matrix-based stability analysis for 2-D Euler equations is performed to explore the cause of instability of numerical schemes. By combining the Roe with HLL flux in different directions and different flux components, we give an interesting explanation to the linear numerical instability. Based on such analysis, some hybrid schemes are compared to illustrate different mechanisms in controlling shock instability. Numerical experiments are presented to verify our analysis results. The conclusion is that the scheme of restricting directly instability source is more stable than other hybrid schemes.

No abstract

No abstract

We construct a monotone finite volume scheme on distorted meshes for multimaterial, nonequilibrium radiation diffusion problems, which are described by the coupled radiation diffusion and material conduction equations. Moreover, we prove theoretically that the scheme is monotone. Numerical results are presented to show that our scheme preserves positivity of solution on various distorted meshes, and the contours of numerical solution obtained by our scheme on distorted meshes accord with that on rectangular meshes. Moreover, numerical tests indicate that our monotone scheme is more computationally efficient than the nine point scheme. These results show that our nonlinear monotone finite volume scheme is a practical and attractive method for solving nonlinear diffusion equations on distorted meshes. Introduction.Radiation transport in astrophysical phenomena and inertial confinement fusion is often modeled using a diffusion approximation. When the radiation field is not in thermodynamic equilibrium with the material, a coupled set of time dependent diffusion equations is used to simulate energy transport, including radiation diffusion and material conduction. These equations are highly nonlinear and tightly coupled and exhibit multiple time and space scales. Hence, it is a challenging problem for us to obtain their numerical solutions with high accuracy.Many authors have studied the efficient and accurate numerical solution of the nonequilibrium radiation diffusion equations [10,11,16,17,18,21,22], and they focus on the high order time integration methods and the nonlinear iteration solution methods on rectangular meshes. The Jacobian-free Newton-Krylov method for solving nonequilibrium radiation diffusion problem is presented in [10]. The authors compare the performance of two different time-step control methods in [11]. The physical-based preconditioning of the nonequilibrium radiation diffusion equations is investigated in [18], and a minor modification to the operator-split preconditioner is given in [16]. The accuracy of time-integration methods for the radiation diffusion equations is studied in [21]. The authors further study the time-integration methods and compare their accuracy and efficiency in [17]. The efficient solution of multidimensional flux-limited nonequilibrium radiation diffusion coupled to material conduction with second-order time discretization is considered in [22]. However, these works mentioned above focus on rectangular meshes. In many application fields, the radiation diffusion problem often couples with the hydrodynamics problem. One often uses the Lagrangian method or arbitrary Lagrangian