Solution Of Inviscid Compressible Flows Research Articles

Numerical simulation of multi-dimensional inviscid compressible flows by using TV-HLL scheme

This paper deals with the numerical solution of inviscid compressible flows. The three-dimensional Euler equations describing the mentioned problem are presented and solved numerically with the finite volume method. The evaluation of the numerical flux at the interfaces is performed by using the Toro Vazquez-Harten Lax Leer (TV-HLL) scheme. An essential feature of the proposed scheme is to associate two systems of differential equations, called the advection system and the pressure system. It can be implemented with a very simple manner in the standard finite volume Euler and Navier–Stokes codes as extremely simple task. The scheme is applied to some test problems covering a wide spectrum of Mach numbers, including hypersonic, low speed flow and three-dimensional aerodynamics applications.

A spectral difference lattice Boltzmann method for solution of inviscid compressible flows on structured grids

In this work, a spectral difference lattice Boltzmann method (SDLBM) is developed and applied for an accurate simulation of two-dimensional inviscid compressible flows on structured grids. The compressible form of the discrete Boltzmann–BGK equation is used in which multiple particle speeds have to be employed to correctly model the compressibility in a thermal fluid. Here, the 2D compressible Lattice Boltzmann (LB) model proposed by Watari is applied. The spectral difference (SD) method is implemented for the solution of the LB equation in which the particle distribution function is stored at the solution points while the fluxes are computed at the flux points for calculating the particle distribution function. For time accurate solutions, the fourth-order Runge–Kutta scheme is used to discretize the temporal term in the LB equation. Note that the procedure of implementing the SD method to solve the LB equation is nearly the same as that procedure developed in the literature for the solution of the Euler equations. The accuracy and robustness of the present solution methodology are demonstrated by simulating different benchmark compressible flow problems. A sensitivity study is also conducted to evaluate the effects of the numerical parameters and the grid size/distribution on the accuracy and performance of the solution. At first, three inviscid compressible flow problems, namely, the stationary isentropic vortex, the shock tube and the shock–vortex interaction are solved by using the SDLBM to demonstrate the accuracy and robustness of the present solution methodology. Results computed for these test cases are in good agreement with the analytical and the available numerical solutions. To more assess the accuracy and robustness of the SDLBM, a third-order finite volume LBM (FVLBM) is also developed and the solutions obtained by these two methods for the test cases simulated are thoroughly compared with each other. It is demonstrated that the SDLBM is more accurate and robust compressible inviscid flow solver that can be used for evaluating the other compressible LB-based flow solvers. As the final problem, the supersonic flow past a bump is simulated to demonstrate the accuracy and robustness of the SDLBM in reaching to a steady-state solution.

Numerical solution of inviscid and viscous laminar and turbulent flow around the airfoil

This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox k-omega model. Calculations are done for NACA 0012 and RAE 2822 airfoil profile for the different angles of upstream flow. Numerical results are compared and discussed with experimental data.

Improvement of a solution of inviscid compressible flows using a mixed wall boundary condition

Boundary conditions have a vital role in the numerical solution of the partial differential equations governing fluid flows, and they have a great influence over the numerical stability and accuracy of the final solutions. One of the most important physical boundary conditions in flow field analysis, especially for inviscid flows, is the wall boundary condition imposed on body surfaces. To solve a three-dimensional compressible Euler equation (with five PDE's), a total of five boundary conditions on the body surface should be prescribed. The wall's velocity magnitude is one of the parameters to be determined, and the way this velocity magnitude is calculated affects the accuracy and stability of the numerical approach. In this paper, four different methods for calculation of the wall velocity magnitude are introduced, tested and compared against several test cases of subsonic and supersonic flows. Since there are many problems where both subsonic and supersonic flows coexist, a mixed boundary condition takes into account the flow Mach number is proposed. The mixed boundary condition is applied to several test cases and the stability of the method is examined.

Numerical solution of inviscid and viscous flow around the profile

This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox’s k-ω model. Calculations are done in GAMM channel computational domain with 10% DCA profile and in turbine cascade computational domain with 8% DCA profile. Numerical methods are based on a finite volume solution and compared with experimental measurements for 8% DCA profile.

Least-squares finite element solution of Euler equations with H-type mesh refinement and coarsening on triangular elements

Purpose – The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows. Design/methodology/approach – Unsteady Euler equations are discretized on meshes of linear and quadratic triangular and quadrilateral elements using LSFEM. Backward Euler scheme is used for time discretization. For the refinement of linear triangular elements, a modified version of the simple bisection algorithm is used. Mesh coarsening is performed with the edge collapsing technique. Pressure gradient-based error estimation is used for refinement and coarsening decision. The developed solver is tested with flow over a circular bump, flow over a ramp and flow through a scramjet inlet problems. Findings – Pressure difference based error estimator, modified simple bisection method for mesh refinement and edge collapsing method for mesh coarsening are shown to work properly with the LSFEM formulation. With the proper use of mesh adaptation, time and effort necessary to prepare a good initial mesh reduces and mesh independency control of the final solution is automatically taken care of. Originality/value – LSFEM is used for the first time for the solution of inviscid compressible flows with h-type mesh refinement and coarsening on triangular elements. It is shown that, when coupled with mesh adaptation, inherent viscous dissipation of LSFEM technique is no longer an issue for accurate shock capturing without unphysical oscillations.

A Mach-uniform pressure correction algorithm using AUSM flux definitions

A collocated finite-volume pressure correction procedure for the solution of inviscid compressible flow at all speeds is presented. Pressure correction methods usually adopt a so-called Rhie-Chow interpolation for the cell face velocities in order to provide pressure-velocity coupling. However, as is shown on the testcase of a one-dimensional transonic nozzle, this Rhie-Chow interpolation becomes highly diffusive in high Mach number flows, resulting in an extreme smearing of the shock. Therefore we replace the Rhie-Chow interpolation for velocity and the central interpolation for pressure by AUSM+ definitions. This results in a much sharper shock capturing, even with a first order scheme. However, the diffusive contributions of this flux scale badly when the Mach number diminishes. Furthermore, pressure-velocity coupling at low Mach numbers has to be provided. These two problems can be resolved by respectively introducing a preconditioned speed of sound and adding a pressure-diffusion component. The latter resembles the artificial dissipation introduced by the Rhie-Chow interpolation, but differently it is turned off when sonic values are reached.

A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow

The paper is concerned with the numerical solution of an inviscid compressible flow with the aid of the discontinuous Galerkin finite element method. Since the explicit time discretization requires a high restriction of the time step, we propose semi-implicit numerical schemes based on the homogeneity of inviscid fluxes, allowing a simple linearization of the Euler equations which leads to a linear algebraic system on each time level. Numerical experiments performed for the Ringleb flow problem verify a higher order of accuracy of the presented method and demonstrate lower CPU-time costs in comparison with an explicit method. Then the method is tested on more complex unsteady Euler flows.