Efficient implicit algorithm for the equations of 2-D viscous compressible flow: application to shock-boundary layer interaction

A high-order accurate unstructured spectral difference lattice Boltzmann method for computing inviscid and viscous compressible flows

A simple distribution function-based gas-kinetic scheme for simulation of viscous incompressible and compressible flows

Enhanced anisotropic block-based adaptive mesh refinement for three-dimensional inviscid and viscous compressible flows

An LU implicit multigrid algorithm is developed to calculate 3-D compressible viscous flows. This scheme solves the full 3-D Reynolds-Averaged Navier-Stokes equation with a two-equation kappa-epsilon model of turbulence. The flow equations are integrated by an efficient, diagonally inverted, LU implicit multigrid scheme while the kappa-epsilon equations are solved, uncoupled from the flow equations, by a block LU implicit algorithm. The flow equations are solved within the framework of the multigrid method using a four-grid level W-cycle, while the kappa-epsilon equations are iterated only on the finest grid. This treatment of the Reynolds-Averaged Navier-Stokes equations proves to be an efficient method for calculating 3-D compressible viscous flows.

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from experiments, field measurements, and large-scale simulations at multiple spatiotemporal scales. Machine learning (ML) offers a wealth of techniques to extract ...Read More

Comparison of numerical methods for the solution of viscous incompressible and low Mach number compressible flow

Very recently, Dang and Gao (Inverse Probl 27:015007, 2011) introduced a KM-CQ algorithm with strong convergence for the split feasibility problem. In this paper, we will continue to consider the split feasibility problem. We present two algorithms. First, we introduce an implicit algorithm. Consequently, by discretizing the continuous implicit algorithm, we obtain an explicit algorithm. Under some weaker conditions, we show the strong convergence of presented algorithms to some solution of the split feasibility problem which solves some special variational inequality. As special cases, we obtain two algorithms which converge strongly to the minimum norm solution of the split feasibility problem. Results obtained in this paper include the corresponding results of Dang and Gao (2011) and extend a recent result of Wang and Xu (J Inequalities Appl 2010, doi:10.1155/2010/102085).

The Reynolds-averaged Navier–Stokes (RANS) equations remain a workhorse technology for simulating compressible fluid flows of practical interest. Due to model-form errors, however, RANS models can yield erroneous predictions that preclude their use on mission-critical problems. This report summarizes work performed from FY22-FY24 focused on improving RANS models for hypersonic flows using data-driven modeling and scientific machine learning. In this work we: 1. Investigate the current capabilities of RANS models in Sandia’s parallel aerodynamics and re-entry code (SPARC) for hypersonic flows with a focus on shock boundary layer interactions (SBLIs), 2. Assess several established corrections that exist in the literature aimed at improving predictions for SBLIs, 3. Develop improved models for the Reynolds stress tensor using tensor-basis neural networks, 4. Develop a neural-network-based variable turbulent Prandtl number model to reduce errors in wall heating in SBLIs. 5. Begin future investigations including employing the LIFE framework to improve wall heating predictions in SBLIs as well as the ensemble Kalman filter. We find that current RANS models in SPARC are deficient for complex SBLI flows. In particular, no current model jointly predicts wall heat flux, wall shear stress, and wall pressure with reasonable accuracy. Existing corrections help, but do not alleviate this issue altogether. The development of improved models for the Reynolds stress tensor via tensor-basis neural networks results in more predictive RANS models across a suite of low-speed and high-speed cases. For hypersonic boundary layers, the inclusion of the wall-normal Reynolds stress via TBNNs has an appreciable impact on the wall-normal momentum balance and wall quantities. However, we find that improvements to the Reynolds stress tensor do not address the over-prediction in wall heat flux in SBLIs. We find that a neural-network-based variable turbulent Prandtl number model systematically and substantially improves wall heating predictions for a range of SBLI cases.

Viscous compressible flow in a semi-sealed porous medium is attracting increasing attention due to recent interest in gas reservoir and energy storage. Such a flow is driven by the volumetric expansion of the fluid, and Darcy's law is no longer applicable as it is fundamentally based on the incompressible flow assumption and for open systems. In the pore space, the compressible flow is governed by a damped wave equation for the density in the linear regime [Jin and Chen, “Fundamental equations for primary fluid recovery from porous media,” J. Fluid Mech. 860, 300–317 (2019)]. In this work, we study viscous compressible flow through a semi-sealed pore network generated from digital rocks, which is a representation of naturally made porous media. The mass depletion rate computed from the pore-scale simulations is then matched to that from a macroscopic effective diffusion model to extract the effective diffusion coefficient. The dependence of the macroscopic diffusion coefficient on the pore network parameters is established. The multiphase distribution during water imbibition process is further simulated by invasion percolation and the macroscopic diffusion coefficient at different water saturation process are calculated. It is shown that the macroscopic diffusion coefficient with multiphase condition is controlled by the interplay of gas-occupied pore structure parameters (pore size, connectivity) and surface wettability. For water-wet case, the macroscopic diffusion coefficient increases with the increasing water saturation and the first-order influence on macroscopic gas flux change can be attributed to the decreasing gas saturation.

Implicit numerical integration of highly nonlinear plasticity models

Discontinuous finite element methods are finding widespread use in a wide range of scientific and technical applications since they are among the few available methods for the approximation of partial differential problems that combines high-order accuracy, geometric flexibility, and robustness. The price to pay for the robustness, accuracy, and flexibility of these methods is their high computational cost and storage requirement. However, the computational efficiency of discontinuous finite element methods can be substantially improved by resorting to multilevel solution techniques. This chapter presents the application of a p-multigrid high-order accurate discontinuous finite element method to the numerical solution of compressible laminar viscous flows (compressible Navier–Stokes equations) and to compressible turbulent flows modeled with the Reynolds-Averaged Navier–Stokes equations coupled with the k-\(\omega \) turbulence model.

Solution of Computational Fluid Dynamics Problems on Parallel Computers with Distributed Memory

A robust, colocated, implicit algorithm for direct numerical simulation of compressible, turbulent flows

A compressible viscous two-phase flow of SF6 and Ar with condensation in a supersonic nozzle is calculated. The flow field is solved with a 3rd-order MUSCL type TVD scheme. The calculation of condensate mass fraction and nucleation rate was based on Becker-Doring's condensation theory. The development of velocity and thermal boundary layer is discussed in detail from the point of view of the interaction between the boundary layer and condensation. Distribution of pressure along the nozzle axis obtained from the numerical calculation is in good accordance with the experimental one in the case of the stagnation pressure region from 20 kPa to 100 kPa. It was found from the result that the condensation takes place in a limited region under relatively high stagnation pressure, which spreads downstream as the stagnation pressure decreases. The temperature and velocity gradients in the boundary layer increase due to the latent heat release of condensation. Consequently, development of the velocity and thermal boundary layers was suppressed by the condensation.

Zonal disturbance region update method for steady compressible viscous flows