Explicit time marching method with enhanced stability

Area of Science:

• Computational Science
• Numerical Analysis
• Distributed Computing

Background:

• Implicit temporal schemes in partial differential equation (PDE) solvers face challenges in parallelization.
• Explicit procedures with enhanced stability limits are gaining traction for complex simulations.
• Asynchronous delayed difference methods offer potential for stability improvements.

Purpose of the Study:

• To introduce and analyze a novel weighted difference scheme for explicit PDE solvers.
• To enhance the stability limits of existing explicit methods.
• To address and overcome instabilities like checkerboard patterns in delayed difference schemes.

Main Methods:

• Modification of an asynchronous delayed difference method.
• Development of a weighted difference scheme as an average of delayed and conventional explicit schemes.
• Numerical analysis to evaluate the attributes and performance of the proposed scheme.

Main Results:

• The weighted difference scheme demonstrates an improved stability limit of 1.5.
• The proposed method effectively mitigates the checkerboard instability.
• Numerical analyses confirm the enhanced stability and performance characteristics.

Conclusions:

• The weighted difference scheme offers a viable enhancement for explicit PDE solvers.
• This method provides a more stable and reliable alternative for complex simulations in distributed computing.
• Further numerical investigations support the practical applicability of the weighted difference scheme.