A New Scheme For Accurate Riemann Solver

Solutions on Narrower Cells over Riemann Fans

A New Scheme for Accurate Riemann Solver

Researchers have developed a new scheme for Riemann solver that retains the advantage of being Riemann-solver. The scheme provides more precise estimates of the width of the Riemann fans, leading to improved accuracy in solving the Riemann problem. This advancement has significant implications for computational fluid dynamics (CFD) and other fields that rely on accurate solutions to partial differential equations.

Admissible Wave Fans and the Riemann Problem

In the context of CFD, the Riemann problem involves finding the solution to a system of hyperbolic partial differential equations at a discontinuity. Riemann solvers are numerical methods used to approximate this solution. The accuracy of Riemann solvers is crucial for obtaining reliable CFD simulations.

The new scheme addresses a key issue in Riemann solvers: the admissibility of wave fans. Wave fans are regions in the solution space where the flow is smooth. In certain situations, shocks can appear within wave fans, leading to non-physical solutions. The new scheme ensures that only admissible wave fans are considered, preventing the occurrence of unphysical shocks.

Improved Accuracy and Efficiency

The more precise estimates of the Riemann fan widths lead to improved accuracy in the solution of the Riemann problem. This improvement is particularly noticeable in cases with complex flow patterns and discontinuities. Additionally, the new scheme is designed to be efficient, making it suitable for large-scale CFD simulations.

Applications in Computational Fluid Dynamics

The new scheme has wide-ranging applications in CFD. It can be used to simulate a variety of fluid flow problems, including those involving shock waves, turbulence, and multi-phase flows. The improved accuracy and efficiency of the scheme make it a valuable tool for researchers and engineers in various fields, such as aerospace engineering, automotive design, and environmental modeling.