The use of limiters may impact both accuracy and resolution of a solution. And the accuracy and resolution are highly dependent on the amount of numerical dissipation in a scheme, so the ability of limiters to control numerical dissipation should be improved. In this view, based on the examination of several classical limiters to control dissipation, a class of general piecewise-linear flux limiters (termed GPL limiters) are presented in this paper for Multi-step time-space-separated unsteady schemes. The GPL limiters can satisfy the second-order TVD criterion and contain some existing limiters such as Superbee and Minmod. Using the decrement of discrete total entropy to represent the amount of numerical dissipation, an entropy dissipation function of GPL limiters is defined with three parameter variables. By proving the monotonicity of this function, a new GPL type limiter (named MDF individually), which can minimize the numerical dissipation and improve the calculation accuracy, is proposed. A high resolution entropy-consistent scheme is obtained by MDF limiter, which will be proved to satisfy entropy stability and entropy consistency. Computational results of this scheme for several 1-D and 2-D Euler test cases are presented, demonstrating the accuracy, monotonicity and robustness of MDF limiter.

Accurate prediction of the flow around multi-element airfoil is a prerequisite for improving aerodynamic performance, but its complex flow features impose high demands on turbulence modeling. In this work, delayed detached-eddy-simulation (DDES) and zonal detached-eddy-simulation (ZDES) was applied to simulate the flow past a three-element airfoil. To investigate the effects of numerical dissipation of spatial schemes, the third-order MUSCL and the fifth-order interpolation based on modified Roe scheme were implemented. From the comparisons between the calculations and the available experimental result, third-order MUSCL-Roe can provide satisfactory mean velocity profiles, but the excessive dissipation suppresses the velocity fluctuations level and eliminates the small-scale structures; DDES cannot reproduce the separation near the trailing edge of the flap which lead to the discrepancy in mean pressure coefficients, while ZDES result has better tally with the experiment.

In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented for the simulation of inviscid and viscous compressible flows. With the finite volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by the conventional smooth function approximation. Unlike the traditional gas-kinetic scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS), the numerical dissipation is controlled with a switch function in the present scheme. That is, the numerical dissipation is only introduced in the region around strong shock waves. As a consequence, the present SF-GKS can well capture strong shock waves and thin boundary layers simultaneously. The present SF-GKS is firstly validated by its application to the inviscid flow problems, including 1-D Euler shock tube, regular shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous transonic and hypersonic flow problems. Good agreement between the present results and those in the literature verifies the accuracy and robustness of SF-GKS.

This study presents a modification of the central-upwind Kurganov scheme for approximating the solution of the 2D Euler equation. The prototype, extended from a 1D model, reduces substantially less dissipation than expected. The problem arises from over-restriction of some slope limiters, which keep slopes between interfaces of cells to be Total-Variation-Diminishing. This study reports the defect and presents a re-derived optimal formula. Numerical experiments highlight the significance of this formula, especially in long-time, large-scale simulations.

The α-function method is a family of second-order explicit methods with controlled numerical dissipation. Thus, it is very promising for the pseudodynamic testing of a system where high frequency responses are of no interest. This is because that favorable numerical dissipation can suppress the spurious growth of high frequency responses, which might arise from numerical and/or experimental errors during a test. Furthermore, the implementation of an explicit method for the pseudodynamic testing is much simpler than for an implicit method. The superiority of using this method in performing a pseudodynamic test was verified both analytically and experimentally. In fact, results of error propagation analysis reveal that the spurious growth of high frequency responses can be suppressed and less error propagation is identified when compared to the Newmark explicit method. Actual tests were conducted pseudodynamically to confirm all the analytical results. It is also illustrated that although the high frequency response is insignificant to the total response it may be significantly amplified and propagated and finally destroys the pseudodynamic test results.