Numerical Issues for Solving Eu-type Generalized Hydrodynamic Equations to Investigate Continuum-rarefied Gas Flows.

Area of Science:

• Computational fluid dynamics
• Kinetic theory
• Numerical methods

Background:

• Generalized hydrodynamic equations derived from Boltzmann kinetic theory are crucial for analyzing continuum and rarefied gas flows.
• The mixed discontinuous Galerkin (DG) method offers a potential numerical approach for solving these complex equations.

Purpose of the Study:

• To investigate and report critical issues in applying the mixed DG method to multidimensional Eu-type generalized hydrodynamic equations.
• To evaluate the method's performance concerning boundary conditions, accuracy, and computational efficiency.

Main Methods:

• Derivation of Eu-type generalized hydrodynamic equations from Boltzmann kinetic theory.
• Implementation of the mixed discontinuous Galerkin method for multidimensional simulations.
• Development and application of a slope limiter for enhanced accuracy and oscillation prevention.
• Comparison of computational efficiency with particle methods.

Main Results:

• Detailed analysis of challenges in treating solid boundary conditions for nonlinear constitutive equations within the mixed DG framework.
• Successful implementation of a slope limiter to maintain high accuracy and prevent unphysical oscillations.
• Demonstration of the method's applicability to complex flow problems, including flow around an airfoil, wedge, sphere, and Apollo configuration.

Conclusions:

• The mixed discontinuous Galerkin method presents viable solutions for simulating complex gas flows governed by Eu-type generalized hydrodynamic equations.
• Addressing boundary conditions, employing slope limiters, and optimizing computational efficiency are key for successful implementation.
• The method shows promise for analyzing challenging aerodynamic configurations.