Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental dat

A Navier-Stokes Solver for Compressible Turbulent Flows on Quadtree and Octree Based Cartesian Grids

Cartesian grids represent a special extent in unstructured grid literature. They employ chiefly created algorithms to produce automatic meshing while simulating flows around complex geometries without considering shape of the bodies. In this article, firstly, it is intended to produce regionally developed Cartesian meshes for two dimensional and three dimensional, disordered geometries to provide solutions hierarchically. Secondly, accurate results for turbulent flows are developed by finite volume solver (GeULER-NaTURe) with both geometric and solution adaptations. As a result, a “hands-off” flow solver based on Cartesian grids as the preprocessor is performed using object-oriented programming. Spalart-Allmaras turbulence model added Reynolds Averaged Navier Stokes equations are solved for the flows around airfoils and wings. The solutions are validated and verified by one two dimensional and one three dimensional turbulent flow common test cases in literature. Both case studies disclose the efficaciousness of the developed codes and qualify in convergence and accuracy

Simulations of Turbulent Flows with Strong Shocks and Density Variations: Final Report

The target of this SciDAC Science Application was to develop a new capability based on high-order and high-resolution schemes to simulate shock-turbulence interactions and multi-material mixing in planar and spherical geometries, and to study Rayleigh-Taylor and Richtmyer-Meshkov turbulent mixing. These fundamental problems have direct application in high-speed engineering flows, such as inertial confinement fusion (ICF) capsule implosions and scramjet combustion, and also in the natural occurrence of supernovae explosions. Another component of this project was the development of subgrid-scale (SGS) models for large-eddy simulations of flows involving shock-turbulence interaction and multi-material mixing, that were to be validated with the DNS databases generated during the program. The numerical codes developed are designed for massively-parallel computer architectures, ensuring good scaling performance. Their algorithms were validated by means of a sequence of benchmark problems. The original multi-stage plan for this five-year project included the following milestones: 1) refinement of numerical algorithms for application to the shock-turbulence interaction problem and multi-material mixing (years 1-2); 2) direct numerical simulations (DNS) of canonical shock-turbulence interaction (years 2-3), targeted at improving our understanding of the physics behind the combined two phenomena and also at guiding the development of SGS models; 3) large-eddy simulations (LES) of shock-turbulence interaction (years 3-5), improving SGS models based on the DNS obtained in the previous phase; 4) DNS of planar/spherical RM multi-material mixing (years 3-5), also with the two-fold objective of gaining insight into the relevant physics of this instability and aiding in devising new modeling strategies for multi-material mixing; 5) LES of planar/spherical RM mixing (years 4-5), integrating the improved SGS and multi-material models developed in stages 3 and 5. This final report is outlined as follows. Section 2 shows an assessment of numerical algorithms that are best suited for the numerical simulation of compressible flows involving turbulence and shock phenomena. Sections 3 and 4 deal with the canonical shock-turbulence interaction problem, from the DNS and LES perspectives, respectively. Section 5 considers the shock-turbulence inter-action in spherical geometry, in particular, the interaction of a converging shock with isotropic turbulence as well as the problem of the blast wave. Section 6 describes the study of shock-accelerated mixing through planar and spherical Richtmyer-Meshkov mixing as well as the shock-curtain interaction problem In section 7 we acknowledge the different interactions between Stanford and other institutions participating in this SciDAC project, as well as several external collaborations made possible through it. Section 8 presents a list of publications and presentations that have been generated during the course of this SciDAC project. Finally, section 9 concludes this report with the list of personnel at Stanford University funded by this SciDAC project

Kartezyen Hesaplama Ağları Kullanılarak Üç Boyutlu Sıkıştırılabilir Akışlar için Navier-Stokes Çözücüsü Geliştirilmesi

TÜBİTAK MAG Proje01.06.2017Bu proje çerçevesinde Kartezyen hesaplama ağları için üç boyutlu bir Navier-Stokes çözücüsü geliştirilmiştir. Hesaplama ağının üretimi ile akış alanının çözümü aşamaları arasında gerekli olan kullanıcı müdahalesini ortadan kaldırmak üzere geliştirilecek yazılımın tam otomatik olarak gerçekleştirilmiştir. Akış alanındaki gövdenin geometrisi yapısal olmayan üçgen elemanlar kullanılarak üç boyutlu bir yüzey hesaplama ağı şeklinde verildiğinde, gövde uyumlu (body-fitted) üçgen prizma elemanlardan oluşan hesaplama ağı gövde geometrisinin şişirilmesiyle otomatik olarak oluşturulmaktadır. Daha sonra, gövde uyumlu hesaplama ağı, çözüm alanının sınırlarını tanımlayan bir kök hücrenin eşit hücrelere bölünmesi ile elde edilen Kartezyen hesaplama ağının içerisine yerleştirilmektedir. Her iki hesaplama ağının arasında kalan bölge dört yüzlü tetrahedral elemanlarla doldurulmaktadır. Navier-Stokes denklemlerinin sonlu hacim formülasyonu hücre merkezli yaklaşımla kullanılmaktadır. Hücre yüzlerindeki akılar akı fark ayrıştırması ve akı vektör ayrıştırması yöntemleriyle hesaplanmaktadır. Uzayda ikinci dereceden doğruluk elde edilebilmesi için basit değişkenlerin yeniden oluşturulmasında (reconstruction) yol tümleme (path integration) ve asgari kareler (least squares) yöntemleri kullanılmaktadır. Doğru ve sınırlı değerler elde edilebilmesi için yeniden oluşturma işlemi sırasında limitleyiciler kullanılmaktadır. Türbülans modeli olarak ise literatürde mevcut modellerden bir denklemli SpalartAllmaras türbülans modeli ile iki denklemli k-e ve k-w türbülans modellerinden yararlanılmaktadır. Yakınsamanın hızlandırılabilmesi için yerel zaman adımlarıyla birlikte çok kademeli (multistage) zaman adımlaması kullanılmaktadır. Çözüme bağlı hesaplama ağı adaptasyonu çözüm ile ağ arasındaki uyumun oluşmasını sağlayarak, akıştaki kritik bölgelerin daha iyi çözümlenmesine olanak sağlamaktadır. Çözüm adaptasyonu kayma tabakalarında hız dönümü, normal ve oblik şoklarda ise hız gradyanı kullanılarak gerçekleştirilmektedir. Geliştirilen yazılım NACA 0012 ve ONERA M6 kanadı etrafındaki üç boyutlu akış için test edilmiş ve elde edilen sayısal sonuçlar literatürde mevcut deneysel sonuçları ile karşılaştırılarak doğrulanmıştır