UnDiFi-2D: An unstructured discontinuity fitting code for 2D grids

UnDiFi-2D, an open source (free software) Unstructured-grid, Discontinuity Fitting code, is presented. The aim of UnDiFi-2D is to model gas-dynamic discontinuities in twodimensional (2D) flows as if they were true discontinuities of null thickness that bound regions of the flow-field where a smooth solution to the governing PDEs exists. UnDiFi-2D therefore needs to be coupled with an unstructured CFD solver that is used to discretize the governing PDEs within the smooth regions of the flow-field. Two different, in-house developed, CFD solvers are also included in the current distribution. The main features of the UnDiFi-2D software can be summarized as follows: Programming Language UnDiFi-2D is written in standard Fortran 77/95; its design is highly modular in order to enhance simplicity of use, maintenance and allow coupling with virtually any existing CFD solver; Usability, Maintenance and Enhancement In order to improve the usability, maintenance and enhancement of the code also the documentation has been carefully taken into account. The git distributed versioning system has been adopted to facilitate collaborative maintenance and code development; Copyrights UnDiFi-2D is a free software that anyone can use, copy, distribute, change and improve under the GNU Public License version 3. The present paper is a manifesto of the first public release of the UnDiFi-2D code. It describes the currently implemented features, which are the result of more than a decade of still ongoing CFD developments. This work is focused on the computational techniques adopted and a detailed description of the main characteristics is reported. UnDiFi-2D capabilities are demonstrated by means of examples test cases. The design of the code allows to easily include existing CFD codes and is aimed at ease code reuse and readability.

[1]  H. Emmons,et al.  The numerical solution of compressible fluid flow problems , 1944 .

[2]  Sergio Pirozzoli,et al.  Shock-Wave–Vortex Interactions: Shock and Vortex Deformations, and Sound Production , 2000 .

[3]  Laszlo Fuchs,et al.  Compact Third-Order Multidimensional Upwind Scheme for Navier–Stokes Simulations , 2002 .

[4]  Gino Moretti,et al.  Thirty-six years of shock fitting , 2002 .

[5]  James Glimm,et al.  Front tracking for hyperbolic systems , 1981 .

[6]  Pradeep Singh Rawat,et al.  On high-order shock-fitting and front-tracking schemes for numerical simulation of shock-disturbance interactions , 2010, J. Comput. Phys..

[7]  M. Hubbard,et al.  Discontinuous upwind residual distribution: A route to unconditional positivity and high order accuracy , 2011 .

[8]  Rémi Abgrall,et al.  High-order residual distribution scheme for the time-dependent Euler equations of fluid dynamics , 2018, Comput. Math. Appl..

[9]  G. Moretti,et al.  A time-dependent computational method for blunt body flows. , 1966 .

[10]  M. Carpenter,et al.  Accuracy of Shock Capturing in Two Spatial Dimensions , 1999 .

[11]  Qiang Zhang,et al.  Three-Dimensional Front Tracking , 1998, SIAM J. Sci. Comput..

[12]  Carl Ollivier-Gooch,et al.  Inserting a Curve into an Existing Two Dimensional Unstructured Mesh , 2013, IMR.

[13]  J. Glimm,et al.  Front-Tracking Methods , 2016 .

[14]  Herman Deconinck,et al.  A Conservative Formulation of the Multidimensional Upwind Residual Distribution Schemes for General Nonlinear Conservation Laws , 2002 .

[15]  Christian Klingenberg,et al.  Front tracking and two dimensional Riemann problems , 2011 .

[16]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[17]  J. Anderson,et al.  Fundamentals of Aerodynamics , 1984 .

[18]  Mikhail S. Ivanov,et al.  Computation of weak steady shock reflections by means of an unstructured shock-fitting solver , 2010 .

[19]  Renato Paciorri,et al.  Shock interaction computations on unstructured, two-dimensional grids using a shock-fitting technique , 2011, J. Comput. Phys..

[20]  Renato Paciorri,et al.  Unstructured Shock-Fitting Calculations of the Transonic Flow in a Gas Turbine Cascade , 2018 .

[21]  Francesco Nasuti,et al.  Steady and Unsteady Shock Interactions by Shock Fitting Approach , 2017 .

[22]  Rémi Abgrall,et al.  High Order Fluctuation Schemes on Triangular Meshes , 2003, J. Sci. Comput..

[23]  Rémi Abgrall,et al.  An ALE Formulation for Explicit Runge–Kutta Residual Distribution , 2014, Journal of Scientific Computing.

[24]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[25]  Jun Liu,et al.  A shock-fitting technique for cell-centered finite volume methods on unstructured dynamic meshes , 2017, J. Comput. Phys..

[26]  X. Zhong,et al.  Direct Numerical Simulation on the Receptivity, Instability, and Transition of Hypersonic Boundary Layers , 2012 .

[27]  Xiaolin Li,et al.  Simple front tracking , 1999 .

[28]  Lingling Wu,et al.  A simple package for front tracking , 2006, J. Comput. Phys..

[29]  Rémi Abgrall,et al.  Toward the ultimate conservative scheme: following the quest , 2001 .

[30]  Jiaying Liu,et al.  An adaptive discontinuity fitting technique on unstructured dynamic grids , 2019, Shock Waves.

[31]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[32]  Philip L. Roe,et al.  Compact high‐resolution algorithms for time‐dependent advection on unstructured grids , 2000 .

[33]  M M Hafez,et al.  Innovative Methods for Numerical Solution of Partial Differential Equations , 2001 .

[34]  Andrea Lani,et al.  SF: An Open Source Object-Oriented Platform for Unstructured Shock-Fitting Methods , 2017 .

[35]  Thomas J. R. Hughes,et al.  Stabilized Methods for Compressible Flows , 2010, J. Sci. Comput..

[36]  Herman Deconinck,et al.  Residual Distribution Schemes: Foundations and Analysis , 2007 .

[37]  Aldo Bonfiglioli,et al.  An unstructured, three-dimensional, shock-fitting solver for hypersonic flows , 2010 .

[38]  P. Alam.  ‘A’ , 2021, Composites Engineering: An A–Z Guide.

[39]  Rémi Abgrall,et al.  Construction of second order accurate monotone and stable residual distribution schemes for unsteady flow problems , 2003 .

[40]  Howard W Emmons.  Flow of a compressible fluid past a symmetrical airfoil in a wind tunnel and in free air , 1948 .

[41]  Per-Olof Persson,et al.  An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions , 2017, J. Comput. Phys..

[42]  Jun Liu,et al.  A Shock-Fitting Technique for ALE Finite Volume Methods on Unstructured Dynamic Meshes , 2017 .

[43]  Sergio Pirozzoli,et al.  Numerical Methods for High-Speed Flows , 2011 .

[44]  Renato Paciorri,et al.  An embedded shock-fitting technique on unstructured dynamic grids , 2021 .

[45]  Parviz Moin,et al.  Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves , 2010, J. Comput. Phys..

[46]  이화영.  X , 1960, Chinese Plants Names Index 2000-2009.

[47]  Jonathan Richard Shewchuk,et al.  Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator , 1996, WACG.

[48]  Eitan Tadmor,et al.  A minimum entropy principle in the gas dynamics equations , 1986 .

[49]  Andrew Corrigan,et al.  A moving discontinuous Galerkin finite element method for flows with interfaces , 2018, International Journal for Numerical Methods in Fluids.

[50]  Philip L. Roe,et al.  A multidimensional generalization of Roe's flux difference splitter for the euler equations , 1993 .

[51]  Brian T. Helenbrook,et al.  A novel stabilization method for high-order shock fitting with finite element methods , 2021, J. Comput. Phys..

[52]  Renato Paciorri,et al.  A mass-matrix formulation of unsteady fluctuation splitting schemes consistent with Roe’s parameter vector , 2013 .

[53]  Ting Song,et al.  The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows , 2018, J. Comput. Phys..

[54]  A. Bonfiglioli,et al.  Convergence Analysis of Shock-Capturing and Shock-Fitting Solutions on Unstructured Grids , 2014 .

[56]  Renato Paciorri,et al.  Unsteady shock‐fitting for unstructured grids , 2016 .

[57]  R. Abgrall,et al.  High Order Schemes for Hyperbolic Problems Using Globally Continuous Approximation and Avoiding Mass Matrices , 2017, J. Sci. Comput..

[58]  M. Dominici.  An Overview of Pandoc , 2014 .

[59]  Thomas D. Economon,et al.  Stanford University Unstructured (SU 2 ): An open-source integrated computational environment for multi-physics simulation and design , 2013 .

[60]  Gino Moretti,et al.  On the matter of shock fitting , 1975 .

[61]  P. L. Roe,et al.  Optimum positive linear schemes for advection in two and three dimensions , 1992 .

[62]  Renato Paciorri,et al.  An unstructured, three-dimensional, shock-fitting solver for hypersonic flows , 2013 .

[63]  Domenic D'Ambrosio,et al.  Numerical Instablilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon , 2001 .

[64]  Rémi Abgrall,et al.  A Lax–Wendroff type theorem for residual schemes , 2001 .

[65]  Mario Ricchiuto,et al.  An explicit residual based approach for shallow water flows , 2015, J. Comput. Phys..

[66]  Herman Deconinck,et al.  Residual distribution for general time-dependent conservation laws , 2005 .

[67]  Tariq D. Aslam,et al.  High-order shock-fitted detonation propagation in high explosives , 2017, J. Comput. Phys..

[68]  Carl Ollivier-Gooch,et al.  Inserting a surface into an existing unstructured mesh , 2016 .

[69]  Per-Olof Persson,et al.  Implicit shock tracking using an optimization-based, r-adaptive, high-order discontinuous Galerkin method , 2020, J. Comput. Phys..

[70]  Renato Paciorri,et al.  Accurate detection of shock waves and shock interactions in two-dimensional shock-capturing solutions , 2020, J. Comput. Phys..

[71]  Danna Zhou,et al.  d. , 1840, Microbial pathogenesis.

[72]  Renato Paciorri,et al.  Basic Elements of Unstructured Shock-Fitting: Results Achieved and Future Developments , 2017 .

[73]  Rémi Abgrall,et al.  Explicit Runge-Kutta residual distribution schemes for time dependent problems: Second order case , 2010, J. Comput. Phys..

[74]  P. Roe.  The 'optimum' upwind advection on a triangular mesh , 1990 .

[75]  Mohamed Mezine,et al.  Construction of second-order accurate monotone and stable residual distribution schemes for steady problems R , 2004 .

[76]  Renato Paciorri,et al.  A shock-fitting technique for 2D unstructured grids , 2009 .

[77]  Rémi Abgrall,et al.  High order methods for CFD , 2017 .

[78]  Qiang Zhang,et al.  Front tracking in two and three dimensions , 1998 .

[79]  Aldo Bonfiglioli,et al.  Fluctuation Splitting Schemes for the Compressible and Incompressible Euler and Navier-Stokes Equations , 2000 .

[80]  Renato Paciorri,et al.  Numerical Simulation of Shock Boundary Layer Interaction Using Shock Fitting Technique , 2019 .

[81]  Herman Deconinck,et al.  Space-time residual distribution schemes for hyperbolic conservation laws on unstructured linear finite elements , 2002 .

[82]  R. D. Richtmyer,et al.  A Method for the Numerical Calculation of Hydrodynamic Shocks , 1950 .

[83]  Oliver A. McBryan,et al.  Front Tracking for Gas Dynamics , 1984 .

[84]  Mirco Ciallella,et al.  Extrapolated Shock Tracking: Bridging shock-fitting and embedded boundary methods , 2020, J. Comput. Phys..

[85]  V. Guinot.  Approximate Riemann Solvers , 2010 .

[86]  Renato Paciorri,et al.  Development of an Unsteady Shock-Fitting Technique for Unstructured Grids , 2014 .

[87]  Herman Deconinck,et al.  Positive matrix distribution schemes for hyperbolic systems, with application to the Euler equations , 1996 .

[88]  A. Bonfiglioli,et al.  TOWARDS A MODULAR APPROACH FOR UNSTRUCTURED SHOCK-FITTING , 2013 .