arXiv subjects

Chun-wei Gu

Publications and source records attributed to Chun-wei Gu.

4 recordsLinked to original sources

arXiv2018

An Improved Roe Scheme for All Mach-Number Flows Simultaneously Curing Known Problems

Roe scheme is known for its good performance in moderate-Mach-number flows. However, this scheme and its extended versions suffers from many disastrous problems, such as non-physical behavior, global cut-off, and checkerboard problems, for incompressible flows; and shock instability, expansion shock, and positively non-conservative problems for hypersonic flows. In this paper, non-physical behavior problem, checkerboard problem, and main reason of shock instability problem are due to that the Roe scheme cannot identify multi-dimensional incompressible and compressible flows when normal Mach number on the cell face tends to zero, and then leads to incorrect cross modifications. Positively non-conservative problem is also identified as another important reason for shock instability. Therefore, Mach number and an assistant pressure-density-varying detector are introduced into the Roe scheme to judge compressibility, positivity condition is satisfied by a simple modification with minimal numerical dissipation increases and even with possible decreases in numerical dissipation, the mechanism of the preconditioned Roe scheme is introduced to suppress checkerboard problem, and modified entropy fix and the rotated Riemann solver is combined with complementary advantages as an assistant improvement for better robust. Based on above improvements and previous developments for global cut-off and expansion shock problems, an improvement Roe scheme for all Mach-number flow (Roe-AM) is proposed to simultaneously overcome nearly all well-known drawbacks of the classical Roe scheme. The Roe-AM scheme is simple, easy to implement, computationally low-cost, robust, good extensibility, and free of empirical parameters essentially, with increasing minimal numerical dissipation.

physics.comp-ph↗

arXiv2016

The Role of Momentum Interpolation Mechanism of the Roe Scheme in the Shock Instability

The shock instability phenomenon is a famous problem for the shock-capturing scheme. By subdividing the numerical dissipation of the Roe scheme, the term of pressure-difference-driven modification for the cell face velocity is regarded as a version of the momentum interpolation method (MIM), which is necessary for incompressible flows to suppress the pressure checkerboard problem. Through the analysis and odd-even decoupling test, it is discovered that MIM plays the most important role on the shock instability. In fact, for non-linear flows MIM should be completely removed, but unexpected MIM is activated on the cell face nearly parallel to the flow for high Mach number flows or low Mach number flows in shock. For such conditions, two coefficients are designed based on local Mach number and a shock detector, respectively, and then the improved Roe scheme is proposed, which gives consideration to requirement of MIM for incompressible and compressible flows and is validated for good performance of avoiding odd-even decoupling. Therefore, the aim of decreasing rather than increasing numerical dissipation to cure the shock instability can be achieved.

physics.flu-dyn↗

arXiv2016

Cures for the Expansion Shock and the Shock Instability of the Roe Scheme

A common defect of the Roe scheme is the production of non-physical expansion shock and shock instability. An improved method with several advantages was presented to suppress the shock instability. However, this method cannot prevent expansion shock and is incompatible with the traditional curing method for expansion shock. Therefore, the traditional curing mechanism is analyzed. The discussion explains the effectiveness of the traditional curing method and identifies several defects, one of which leads to incompatibility between curing the shock instability and expansion shock. Consequently, a new improved Roe scheme is proposed in this study. This scheme is concise, easy to implement, low computational cost, and robust. More importantly, the scheme can simultaneously cure the shock instability and expansion shock without additional costs.

physics.flu-dyn↗

arXiv2011

On the Mechanism of Roe-type Schemes for All-Speed Flows

In recent years, Roe-type schemes based on different ideas have been developed for all-speed flows, such as the preconditioned Roe, the All-Speed Roe, Thornber's modified Roe and the LM-Roe schemes. This work explores why these schemes succeed or fail with the accuracy and checkerboard problems. Comparison and analysis show that the accuracy and checkerboard problems are caused by the order of the sound speed being too large and too small in the coefficients of the velocity-derivative and pressure-derivative dissipation terms, respectively. These problems can be resolved by choosing coefficients with zero-order sound speed. In addition, to avoid the negative effects of the global cut-off strategy on accuracy while maintaining computational stability, the sound speed terms in the numerator of the coefficients can be determined by local variables, while those in the denominator remain the global cut-off. Two novel schemes are proposed as examples to demonstrate how these ideas can be applied to construct more satisfactory schemes for all-speed flows. Asymptotic analysis and numerical experiments support the theoretical analysis and the rules obtained in the work.

math.NA↗