scholarly journals High-order fully implicit solver for all-speed fluid dynamics

Shock Waves ◽  
2018 ◽  
Vol 29 (5) ◽  
pp. 651-689 ◽  
Author(s):  
R. Nourgaliev ◽  
P. Greene ◽  
B. Weston ◽  
R. Barney ◽  
A. Anderson ◽  
...  
Author(s):  
Robert Nourgaliev ◽  
Patrick T. Greene ◽  
Samuel P. Schofield

A new high-order sharp treatment of mixed cell solutions is introduced. The method is based on the reconstructed discontinuous Galerkin (rDG) scheme, in which we embed the known interfacial jump conditions as additional (physics-based) constraints in the least-squares reconstruction of the high-order degrees of freedom for multiple solution fields in the interfacial (mixed) cells. The approach allows us to avoid direct differentiation across multi-material interfaces, thus providing a robust and high-order accurate solution procedure. To track the interface dynamics, the method is combined with a hybrid of the level set (LS) and the front tracking (FT) methods — the so-called “Marker-Re-Distancing” (MRD) approach. As a fluid solver, we utilize the recently developed fully-implicit reconstructed discontinuous Galerkin method, developed for efficient and high-order resolution of all-speed compressible fluid dynamics. The new sharp physics-based reconstruction is incorporated into the overall Newton-Krylov-based solution procedure, with the residual of the mixed cell representing conservation of the mass, momentum and energy for the mixture. Thus, upon a convergence of the non-linear iterations, our treatment of interfacial cells is conservative.


Author(s):  
André Ribeiro de Barros Aguiar ◽  
Carlos Breviglieri ◽  
Fábio Mallaco Moreira ◽  
Eduardo Jourdan ◽  
João Luiz F. Azevedo

2016 ◽  
Vol 202 ◽  
pp. 12-22 ◽  
Author(s):  
Bartosz D. Wozniak ◽  
Freddie D. Witherden ◽  
Francis P. Russell ◽  
Peter E. Vincent ◽  
Paul H.J. Kelly

Author(s):  
Shivam Singhal ◽  
Yayati Gupta ◽  
Ashish Garg

The computing power of smartphones has not received considerable attention in the mainstream education system. Most of the education-oriented smartphone applications (apps) are limited to general purpose services like Massive Open Online Courses (MOOCs), language learning, and calculators (performing basic mathematical calculations). Greater potential of smartphones lies in educators and researchers developing their customized apps for learners in highly specific domains. In line with this, we present Fluid Dynamics, a highly accurate Android application for measuring flow properties in compressible flows. This app can determine properties across the stationary normal and oblique shock, moving normal shock and across Prandtl $-$ Meyer expansion fan. This app can also measure isentropic flows, Fanno flows, and Rayleigh flows. The functionality of this app is also extended to calculate properties in the atmosphere by assuming the International Standard Atmosphere (ISA) relations and also flows across the Pitot tube. Such measurements are complicated and time-consuming since the relations are implicit and hence require the use of numerical methods, which give rise to repetitive calculations. The app is an efficient semi-implicit solver for gas dynamics formulations and uses underlying numerical methods for the computations in a graphical user interface (GUI), thereby easing and quickening the learning of concerned users. The app is designed for the Android operating system, the most ubiquitous and capable surveillance platform, and its calculations are based on JAVA based code methodology. In order to check its accuracy, the app's results are validated against the existing data given in the literature.


2005 ◽  
Vol 19 (28n29) ◽  
pp. 1483-1486 ◽  
Author(s):  
HAI-QING SI ◽  
TONG-GUANG WANG ◽  
XIAO-YUN LUO

A fully implicit unfactored algorithm for three-dimensional Euler equations is developed and tested on multi-block curvilinear meshes. The convective terms are discretized using an upwind TVD scheme. The large sparse linear system generated at each implicit time step is solved by GMRES* method combined with the block incomplete lower-upper preconditioner. In order to reduce the memory requirements and the matrix-vector operation counts, an approximate method is used to derive the Jacobian matrix, which only costs half of the computational efforts of the exact Jacobian calculation. The comparison between the numerical results and the experimental data shows good agreement, which demonstrates that the implicit algorithm presented is effective and efficient.


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