A Modified Characteristic-Compression Embedded Discontinuity Indicator Based on Artificial Intelligence

Abstract

The high-order and high-resolution numerical schemes are one of the most effective computational methods for simulating high-speed complex flows with shock waves, and the detection of discontinuous structures such as shock waves is one of the key problems in designing robust, high-resolution and high-order numerical schemes. Based on the prior mathematical knowledge and the artificial neural network (ANN) method, a modified characteristic-compression embedded discontinuity indicator was developed to improve the accuracy of discontinuity capturing in the framework of high-order schemes. The present indicator was obtained by pre-modeling based on the prior mathematical knowledge and then learning the undetermined parameters in the model through data-driven methods. This makes the discontinuity indicator concise, and has the advantage of small sample dependency during the training process, and makes the trained model have excellent properties such as low computational complexity and mathematical interpretation. Its one-dimensional form can be naturally generalized to multi-dimensional system of equations on unstructured grids. The present indicator was proved to contain two types of discontinuity capture mechanisms, namely, shock wave capture mechanism based on characteristic compression, and expansion wave origin/contact wave capture mechanism based on large gradient jump. A number of numerical results verified the accuracy of the proposed indicator for capturing different types of discontinuities in high-speed complex flows.

Keywords

• artificial intelligence
• hyperbolic conservation laws
• numerical simulation for high-speed flows
• high-resolution numerical scheme
• discontinuity indicator