A kernel derivative free SPH method - Dongyan Feng; Rahmatjan Imin (Results in Applied Mathematics, 2023)
Based on smooth particle hydrodynamics (SPH) method, this paper proposes the concept of kernel function moment and studies its properties, and puts forward the KDF-SPH (Kernel Derivative Free SPH: KDF-SPH) method. The method proposed in this paper is applied to the calculation of derivatives of one-dimensional functions and partial derivatives of two-dimensional functions, and the numerical simulation of one-dimensional burgers equations and two-dimensional burgers equations. At the same time, the convergence of KDF-SPH method and SPH method is analyzed and compared. The errors of the KDF-SPH method with different kernel functions are compared with those of the SPH method. It turns out that the KDF-SPH method has higher accuracy and better convergence than the traditional SPH method, and the new method proposed in this paper needs less computation because it does not need to solve the derivative of the kernel function. And, it is also effective in reducing the error and improving the stability.