Coefficient datasets for high-order, stable, and conservative boundary schemes for central and compact finite...

Area of Science:

• Numerical Analysis
• Computational Fluid Dynamics
• Scientific Computing

Background:

• Developing stable and conservative numerical boundary schemes is crucial for accurate simulations using finite difference methods.
• Tuning parameters for high-order schemes (4th, 6th, and 8th) is essential for maintaining stability in computational models.
• Existing methods often require significant parameter tuning, impacting simulation efficiency and reliability.

Purpose of the Study:

• To present and validate stable and conservative numerical boundary schemes for compact and explicit finite difference methods.
• To provide specific coefficient values for 4th, 6th, and 8th order boundary schemes.
• To demonstrate the stability and performance of these schemes through rigorous numerical testing.

Main Methods:

• Implementation of 4th, 6th, and 8th order numerical boundary schemes for finite difference approximations.
• Conducting numerical tests on various hyperbolic systems, including constant and varying coefficient equations.
• Utilizing the compressible Euler equations to simulate inviscid vortex transport.

Main Results:

• The article provides explicit coefficients for the 4th, 6th, and 8th order boundary schemes.
• Numerical tests confirm the stability of the proposed schemes across different hyperbolic systems.
• Error norms are documented for various grid resolutions and time-step constraints, available in accompanying databases.

Conclusions:

• The presented boundary schemes offer a stable and conservative approach for high-order finite difference methods.
• The provided coefficients and numerical validation facilitate the practical application of these schemes.
• This work contributes to more reliable and accurate computational simulations in fluid dynamics and other fields.