Comparison of a modified large-particle method with some high resolution schemes. Two-Dimensional test problems

Исследуются вычислительные свойства предложенной ранее новой модификации метода крупных частиц на основе нелинейной коррекции искусственной вязкости на первом (эйлеровом) этапе и гибридизации потоков на втором (лагранжевом и заключительном) этапе, дополненной двухшаговым алгоритмом РунгеКутты по времени. Метод обладает вторым порядком аппроксимации по пространству и времени на гладких решениях. На примере тестовых задач сверхзвукового потока газа в канале со ступенькой и двойного маховского отражения подтверждена работоспособность и вычислительная эффективность метода в сравнении с современными схемами высокой разрешающей способности. A number of computational properties of the previously proposed new modification of a largeparticle method are studied on the basis of a nonlinear correction of artificial viscosity at the first (Eulerian) stage and a hybridization of fluxes at the second (Lagrangian and final) stage supplemented by a twostep RungeKutta algorithm in time. The method has a second order of approximation in space and time on smooth solutions. The computational efficiency of the method is shown compared to several modern high resolution schemes using the forward facing step problem and the double Mach reflection problem.

Osher Flux with Entropy Fix for Two-Dimensional Euler Equations

We compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: A first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.

Piecewise Polynomial Mapping Method and Corresponding WENO Scheme with Improved Resolution

Abstract. The method of mapping function was first proposed by Henrick et al. [J. Comput. Phys. 207:542-547 (2005)] to adjust nonlinear weights in [0,1] for the fifth order WENO scheme, and through which the requirement of convergence order is satisfied and the performance of the scheme is improved. Different from Henrick’s method, a concept of piecewise polynomial function is proposed in this study and corresponding WENO schemes are obtained. The advantage of the new method is that the function can have a gentle profile at the location of the linear weight (or the mapped nonlinear weight can be close to its linear counterpart), and therefore is favorable for the resolution enhancement. Besides, the function also has the flexibility of quick convergence to identity mapping near two endpoints of [0,1], which is favorable for improved numerical stability. The fourth-, fifth- and sixth-order polynomial functions are constructed correspondingly with different emphasis on aforementioned flatness and convergence. Among them, the fifth-order version has the flattest profile. To check the performance of the methods, the 1-D Shu-Osher problem, the 2-D Riemann problem and the double Mach reflection are tested with the comparison of WENO-M, WENO-Z and WENO-NS. The proposed new methods show the best resolution for describing shear-layer instability of the Riemann problem, and they also indicate high resolution in computations of double Mach reflection, where only these proposed schemes successfully resolved the vortex-pairing phenomenon. Other investigations have shown that the single polynomial mapping function has no advantage over the proposed piecewise one, and it is of no evident benefit to use the proposed method for the symmetric fifth-order WENO. Overall, the fifth-order piecewise polynomial and corresponding WENO scheme are suggested for resolution improvement.

Discontinuous Galerkin Solution of Three-Dimensional Reynolds-Averaged Navier-Stokes Equations With S-A Turbulence Model

In this paper Discontinuous Galerkin Method (DGM) is applied to solve the Reynolds-averaged Navier-Stokes equations and S-A turbulence model equation in curvilinear coordinate system. Different schemes, including Lax-Friedrichs (LF) flux, Harten, Lax and van Leer (HLL) flux and Roe flux are adopted as numerical flux of inviscid terms at the element interface. The gradients of conservative variables in viscous terms are constructed by mixed formulation, which solves the gradients as auxiliary unknowns to the same order of accuracy as conservative variables. The methodology is validated by simulations of double Mach reflection problem and three-dimensional turbulent flowfield within compressor cascade NACA64. The numerical results agree well with the experimental data.

Transverse waves in numerical simulations of cellular detonations

In this paper the structure of strong transverse waves in two-dimensional numerical simulations of cellular detonations is investigated. Resolution studies are performed and it is shown that much higher resolutions than those generally used are required to ensure that the flow and burning structures are well resolved. Resolutions of less than about 20 numerical points in the characteristic reaction length of the underlying steady detonation give very poor predictions of the shock configurations and burning, with the solution quickly worsening as the resolution drops. It is very difficult and dangerous to attempt to identify the physical structure, evolution and effect on the burning of the transverse waves using such under-resolved calculations. The process of transverse wave and triple point collision and reflection is then examined in a very high-resolution simulation. During the reflection, the slip line and interior triple point associated with the double Mach configuration of strong transverse waves become detached from the front and recede from it, producing a pocket of unburnt gas. The interaction of a forward facing jet of exploding gas with the emerging Mach stem produces a new double Mach configuration. The formation of this new Mach configuration is very similar to that of double Mach reflection of an inert shock wave reflecting from a wedge.