Spurious oscillations reduction in transient diffusion and wave propagation problems discretized with the Finite...

Area of Science:

• Computational Mathematics
• Numerical Analysis
• Scientific Computing

Background:

• Spurious oscillations commonly occur in numerical solutions, particularly with discontinuities.
• Existing methods often require approximations for functions like the Dirac delta function.
• Accurate solutions for problems with impulsive sources are crucial in various scientific domains.

Purpose of the Study:

• Introduce a new numerical method, SOR-FEM, to mitigate spurious oscillations.
• Enable accurate numerical solutions for problems with impulsive point sources.
• Validate the efficacy of SOR-FEM using established physical problems.

Main Methods:

• Developed the Spurious Oscillation Reduction-Finite Element Method (SOR-FEM).
• Employed analytical solutions of simpler problems to guide numerical solutions of complex ones.
• Applied the Finite Element Method (FEM) for problem-solving.

Main Results:

• Successfully reduced spurious oscillations in numerical solutions.
• Achieved accurate solutions for problems with impulsive point sources without Dirac delta approximations.
• Demonstrated the method's effectiveness on heat diffusion and wave propagation problems.

Conclusions:

• The SOR-FEM is an effective technique for reducing spurious oscillations in numerical simulations.
• The method provides accurate solutions for problems involving impulsive sources.
• SOR-FEM offers a robust approach for complex problems in heat diffusion and wave propagation.