Hypersonic Viscous Flows Simulation with MDG-ICE Method

核心概念

MDG-ICE method optimizes grid for accurate hypersonic flow simulation.

摘要

The Moving Discontinuous Galerkin Method with Interface Condition Enforcement (MDG-ICE) is a high-order method that weakly enforces conservation and interface conditions for accurate flow simulation. An optimization solver based on the Levenberg-Marquardt algorithm enhances robustness and prevents cell degeneration. MDG-ICE formulation applied to challenging test cases yields accurate, oscillation-free results. Anisotropic grid regularization inhibits grid motion in directions with small element length scales. The method adapts the grid to fit shocks and resolve smooth regions without artificial dissipation. The nonlinear solver incorporates increment limiting and adaptive, elementwise regularization to prevent cell degeneration. Results show successful resolution of viscous shocks with highly symmetric surface heat-flux profiles.

統計資料

MDG-ICE is a high-order, r-adaptive method.
An optimization solver based on the Levenberg-Marquardt algorithm enhances robustness.
MDG-ICE formulation applied to challenging test cases yields accurate, oscillation-free results.

引述

"MDG-ICE adapts the grid to satisfy the weak form, repositioning grid interfaces to fit unknown shocks."
"Anisotropic grid regularization inhibits grid motion in directions with small element length scales."

從以下內容提煉的關鍵洞見

The Moving Discontinuous Galerkin Method with Interface Condition Enforcement for the Simulation of Hypersonic, Viscous Flows

by Eric J. Chin... 於 arxiv.org 03-11-2024

https://arxiv.org/pdf/2311.00701.pdf

深入探究

How does MDG-ICE compare to traditional shock capturing approaches

MDG-ICE differs from traditional shock capturing approaches in its unique treatment of the grid as a variable and its implicit shock fitting capabilities. Unlike traditional methods that rely on artificial dissipation or limiting to capture shocks, MDG-ICE adapts the grid geometry to fit high-gradient flow features implicitly. This approach allows MDG-ICE to compute highly accurate high-order solutions without introducing low-order errors associated with artificial stabilization. By simultaneously solving for the flow field and adjusting the grid to fit shocks and resolve smooth regions, MDG-ICE can handle complex shock dynamics more effectively than traditional methods.

What are the implications of the adaptive, elementwise regularization strategy

The adaptive, elementwise regularization strategy in MDG-ICE plays a crucial role in maintaining grid validity and preventing cell degeneration, especially in the presence of highly anisotropic, curved elements that form to resolve sharp viscous features. This strategy involves automatically adjusting the regularization coefficients in an elementwise manner until the solver can proceed with a valid grid. By dynamically scaling the regularization terms based on the local element properties, the strategy ensures that the grid remains valid at every iteration, preventing issues such as negative Jacobian determinants and grid degeneration. This adaptive approach enhances the robustness of the solver and facilitates the resolution of high-gradient features in the flow.

How can MDG-ICE be applied to other fluid dynamics simulations beyond hypersonic flows

MDG-ICE can be applied to a wide range of fluid dynamics simulations beyond hypersonic flows by leveraging its high-order, r-adaptive capabilities and implicit shock fitting methodology. The method's ability to handle complex shock dynamics and resolve sharp gradients makes it suitable for simulations involving viscous flows, boundary layers, and shocks in various flow regimes. MDG-ICE can be utilized in simulations of aerodynamics, combustion, heat transfer, and other fluid dynamics phenomena where accurate resolution of high-gradient features is essential. Its flexibility and robustness make it a valuable tool for researchers and engineers working on a diverse set of fluid dynamics problems.