Extended particle difference method for weak and strong discontinuity problems: part II. Formulations and applications for various interfacial singularity problems

The Extended Particle Difference Method is developed for interfacial singularity problems based on the Extended Particle Derivative Approximation scheme. Node-wise strong formulations are adopted for transient heat transfer problems, potential problems, and elasticity problems with various interfacial boundaries. The governing partial differential equations are directly discretized at interior and boundary nodes and the interface condition is immersed in the derivative approximation or is enforced at interfacial points. Assemblage of the discretized equations generates a linear algebraic system of equations, which accelerates computation speed due to the avoidance of numerical integration. Solving the system gives the nodal solution together with the jump solutions. We also demonstrate the robustness and effectiveness of the developed method with various numerical examples. Despite the existence of the singularity in the solution fields, the method overcomes the geometrical complexity inherent in interface modeling and thus achieves the second-order accuracy.