Third-Order Hyperbolic Navier-Stokes Solver for Unsteady Simulations with Adaptive Space-Time Unstructured Grids
Abstract
The objective of the proposed research is to develop a third-order hyperbolic Navier-Stokes (HNS) solver on adaptive space-time unstructured grids towards barrier-breaking unsteady simulations over moving bodies in future high-performance computing machines with ever- increasing parallelism. The objective is achieved by five key components: (1)an adaptive space-time approach to address the need to exploit concurrency by allowing a larger-degree of parallelism, (2)third-order edge-based discretization to minimize the cost of obtaining high-order accuracy and to allow degenerate zero/negative-volume elements for robustness, (3)implicit gradient algorithms to develop a robust and efficient nonlinear solver on highly- irregular adaptive space-time grids, (4)Jacobian-Free Newton-Krylov solver with an improved Jacobian and nonlinear controls for robust iterative convergence, (5)a space-time HNS formulation to achieve accurate gradients (e.g., viscous stresses, heat fluxes, vorticity) on highly-irregular adaptive space-time grids, on which conventional gradient reconstruction methods such as least-squares methods are known to suffer from oscillations. Space-time methods have significant advantages over traditional time-marching methods in that they allow much larger degrees of parallelism, are high-order and unconditionally stable on arbitrary grids, and simplify moving/deforming-body simulations with a static space-time grids. Space-time methods are made efficient especially with anisotropic grid adaptation. However, to perform such simulations, a very robust nonlinear solver and accurate discretization methods are required that can deal with highly skewed irregular grids. In particular, accurate gradient prediction on such grids has been recognized as one of the most difficult problems in unstructured-grid simulations. Recent studies have demonstrated that the HNS method, being radically different from conventional methods, has a great potential for producing highly accurate gradients on such irregular grids typical in adaptive space-time grids. Also, the third-order edge-based method has a great potential for allowing zero/negative volume elements to bring various advantages and increase robustness. In the proposed research, a robust and accurate HNS edge-based space-time solver will be developed and demonstrated for 2D unsteady flows with adaptive tetrahedral grids in space- time domains, with extensions to 3D unsteady problems ensured in each component. This effort is proposed to build a foundation for a bigger effort of solving real-world 3D unsteady problems in 4D space-time grids.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 06, 2019
- Source ID
- W911NF1910429
Entities
People
- Hiroaki Nishikawa
Organizations
- Army Contracting Command
- National Institute of Aerospace
- United States Army