ExactPack: A Master Code of Exact Solutions for Code Verification

Transcription

1 ExactPack: A Master Code of Exact Solutions for Code Verification Robert L. Singleton Jr. Los Alamos National Laboratory bobs1@lanl.gov Collaborators: Scott Doebling Daniel Israel James Kamm ASME V&V Symposium 2014 Los Vegas, NV 7-9 May 2014 Slide 1

2 Exact Solutions used to Verify Hydro Codes, i.e. dynamic compressible fluid codes Sedov test the conversion of internal energy to kinetic energy First used as a model for the relation between source energy and shock distance and yield estimation, à la Taylor (1945). An equally common test problem: set up continues to engender debate, more complicated to evaluate, illuminates particular algorithm features (particularly near the shock). Noh test the conversion of kinetic energy to internal energy The issue of wall heating is clearly manifested in this problem. A workhorse test problem: easy to set up, easy to evaluate, illuminates particular algorithm features (at the boundary, near the shock). Riemann Cog8 Slide 2

3 After selecting a problem, e.g. Sedov: - Find an exact solution code to a problem, e.g. sedov.f - internet (cococubed.asu.edu) - write one yourself - ask a friend - Create user interface - Run code and plot data - Compare against the hydro code This can be a long and error prone process itself! Slide 3

4 ExactPack integrates this process into a single stand-alone python package - Exact solutions library - Python API integrates the solution library into a common framework: (a) import into your own scripts, (b) GUI or (c) command line control ExactPack sedov.f f2py setup.py other_tools.py sedov.py % cd ExactPack/ % python setup.py build % python setup.py test % python setup.py install noh.f f2py noh.py new.f f2py new.py Slide 4

5 Example Methodology Start with Euler s Equations (dynamical compressible fluid equations). The hydro code solves these equations using sophisticated algorithms. Use simplifying assumptions to find an exact solution, e.g. spherical symmetry (reduces problem to 1D). Code the exact solution and compare flow fields with those from the hydro code. Slide 5

6 Example of an Exact Solution to Euler s Equations Mass density Fluid velocity Specific internal energy State variables (1+3+1=5) Equation of State Pressure 1 equation (mass) 3 equation (momentum) 1 equation (energy) EQ s(5) + IC s + BC s Unique Solution Slide 6

7 Spherically Symmetric Blast Wave: Sedov 1959 Instantaneous release energy E0 at the origin Spherically symmetric Euler Equations E0 polytropic ideal gas EOS: p = ( γ 1) ρe ρ 0 Use Dimensional Analysis! ξ is dimensionless E 0 r = ξ ρ 0 1/5 2/5 t r ± t d dξ PDE s can be expressed as ODE s Slide 7

8 Sedov Blast Wave Timmes and Kamm s exact solution code: sedov.f Their code does not require numerical integration of the ODE s, but only: - root finder (shock position) r shock E 0 = αρ0 1/5 t 2/5-1D numerical quadrature (energy) E 0 4π r s 2 2 = + 0 drr 1 p ρu 2 γ 1 α = I + I 1 2 Slide 8

9 Exact Solution to the Sedov Problem Convention: E0= erg and γ =1.4 gives rshock=1cm at t=1s Slide 9

10 Adding a Solver to ExactPack ExactPack/src/timmes/sedov/sedov.f subroutine sed_1d(time, nstep, xpos, eblast, gam0, den, ener, pres, vel, cs) cf2py intent(out) :: den, ener, pres, vel, cs cf2py intent(hide) :: nstep cf2py integer :: nstep cf2py real*8 :: time, xpos(nstep) cf2py real*8 :: eblast, gamma, cf2py real*8 :: den(nstep), ener(nstep), pres(nstep), cf2py real*8 :: vel(nstep), cs(nstep) c Timmes and Kamm s original source code: integer nstep real*8 time, xpos(*), eblast, gam0,... real*8 den(*), ener(*), pres(*), do i=1,nstep den(i)=0! ener(i)=0!...! enddo gamma = gam0 gamm1 = gamma - 1.q0 gamp1 = gamma + 1.q0... v2 = 2.d0 / (xg2 + gamp1)! Initialize solution! post shock location vstar = 2.q0 / (gamm1*xgeom + 2.q0)! v2 and sing point ExactPack/exactpack/sedov/timmes.py class Sedov(ExactSolver) def _run(self, r, t) den, ener, pres, vel, cs = sed_1(time=t, xpos=r, eblast=self.eblast, gam0=self.gamma, ) import exactpack.sedov.timmes solver = exactpack.sedov.timmes.sedov(eblast= , geometry=3, gamma=1.4) r = numpy.linspace(0.0, 1.2, 1000) t = 1.0 soln = solver(r, t) soln.plot_all() lstandard =.false.! set logicals for lsingular =.false.! solution type lvacuum =.false if (abs(v2 - vstar).le. osmall) then... Slide 10

11 ExactPack Summary Exact Solution Library f90, f, py, c, ExactPack/src/ sedov.f noh.f90 and noh.py cog8.f90 riemann_kamm.f riemann_timmes.f90 rmtv.f guderley/ makefile guderley_1d.f suolson.f f2py Python Interface Code ExactPack/ sedov/sedov.py riemann/riemann.py cog8/cog8.py noh/noh.py sedov/sedov.py suolson.py Fill the 2d Grid: algorithm type vs. physics problem Slide 11

12 Python script to plot sedov from ExactPack import exactpack.sedov.timmes solver = exactpack.sedov.timmes.sedov(eblast= , geometry=3, gamma=1.4) r = numpy.linspace(0.0, 1.2, 1000) t = 1.0 soln = solver(r, t) soln.plot_all() soln.dump( sedov_exact.dat ) Slide 12

13 Abstract For code verification on compares code output against known exact solutions. There are man exact solutions used in this capacity, such as the Noh and Sedov problems. Such exact solution codes are usually stand-alone programs that can be downloaded from the web, after which the user must roll out his or her own plotting package and analysis utilities. When comparing across multiple codes, this can be a time consuming and error prone process. ExactPack is a new utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in fortran or python. The spatial profiles of the relevant gas quantities, such as density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or graphical user interface, and a number of analysis tools and unit tests are provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExacpPack s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable fashion. Slide 13