Finite Volume Code

1. Finite Volume Code Tim Handy

2. Goals • Modular Code – Didn’t want to have to rework all of my code to add a new feature • Dynamic Variables/Functions – Minimal assumptions about code requirements apriori • No anticipation of special variables required for a particular method • Ability to use scriptable C (Ch) for non-constant, analytic input conditions • Try some stuff I don’t normally do

3. High Level Simulation Mesh Initial Conditions Boundary Conditions Interpolation Advection Output Cell

4. 1-Dimensional Level Simulation1D Mesh1D - Uniform1D Initial Conditions (In Progress) Boundary Conditions - Periodic1D Interpolation - Interpolation1D Advection - Advection1D Output Cell1D

5. Simulation1D class Simulation1D : public Simulation { protected: Mesh1D* mesh; BoundaryCondition1D* bc; InitialCondition* ic; Advection1D* advect; Interpolation1D* interp; Output* output; std::string resultsfile; std::map<std::string, std::string> solvers; std::multimap<int,outputinfo*> write_info; . . . }; • Primary constructor takes an input file as an argument and sets up other classes • Abusing polymorphism as much as possible • Simvars is a C++ Map of string->double • Allows for dynamic addition/removal of variables, clear accessing (no need to remember array indices) • Stores generic information other classes may require or are pertinent at the simulation level • Solvers maps a string->string • “interpolation”->”PPM”, “advection”->”Euler” • Allows easy input file parsing (no need for 40 cases for different variables)

6. Mesh1D class Mesh1D : public Mesh { public: Cell1D** cells; intnum_ghost; intindex_lb, index_ub; intNtotal; . . . }; • Holds array (probably change to vector ASAP) of Cell1Ds (Total size = Ncells + 2*num_ghost) • Makes no assumptions about distribution of cells, just here to hold generic information and generic function calls/virtual functions • In 1D case, holds information on

7. Cell1D class Cell { protected: int index; std::map<char,Cell*> neighbors; public: std::map<std::string,double> vars; … }; class Cell1D : public Cell { public: double xl, xr, xc, dx; double A; void populate_vars() { vars["density"] = 0.0; vars["density_w"] = 0.0; vars["density_e"] = 0.0; vars["xl"] = this->xl; vars["xr"] = this->xr; vars["xc"] = this->xc; vars["dx"] = this->dx; vars["A"] = this->A; vars["vx"] = 0.0; vars["vx_e"] = 0.0; vars["vx_w"] = 0.0; } void add_var(std::string var, double val); void remove_var(std::string var);

8. Interpolation1D class Interpolation1D { private: typedef void(*ptr2Interp)(Mesh1D*,double,std::string); public: std::map<std::string, void (*)(Mesh1D*,double,std::string)> func_ptrs; Interpolation1D() { // probably need to be a bit safer here func_ptrs["FOU"] = FOupwind1D; func_ptrs["SOU"] = linear_upwind1D; func_ptrs["PPM"] = PPM; func_ptrs["PPMnonmono"] = nonmonoPPM; } … }; • Interpolation 1D contains the First Order, Second Order, and PPM schemes that operate on a given mesh for a given variable • Contains a map of strings->function pointers (Member functions are made static to make this easy) • Essentially just a wrapper for a set of functions, but allows easy modularity

9. Input File N 64 CFL 0.25 tmin 0 tmax 6.283185307180 V0 -1 xmin 0 xmax6.283185307180 maxiter 3000 solver interpolation PPMnonmono write density.dat density 1 write velocity.dat vx 4 write xc.dat xc 1

10. How to Run a Simulation Simulation1D* sim = new Simulation1D(in); sim->simulate(); … void simulate() { this->t = this->simvars["tmin"]; double Tmax = this->simvars["tmax"]; int iteration = 0; do { iteration++; double dt = this->stable_timestep(); this->set_timestep(dt); this->t += dt; if(this->t > Tmax) { dt -= this->t-Tmax; this->t = Tmax; } std::string interp_method = this->solvers["interpolation"]; interp->run(interp_method, this->mesh, dt, "density"); std::string advect_method = this->solvers["advection"]; advect->run(advect_method, this->mesh, dt, "density"); this->write_output(iteration); }while(t<Tmax && iteration < this->simvars["maxiter"]); }

11. Temporal Rate of Convergence

12. Spatial Rate of Convergence

13. Limited Visible Change

14. Current/Future Work • Rework InitialCondition/BoundaryCondition + Source terms to utilize scriptable C functions using Ch for MMS & incorporate Automatic Differentiation library • Minor code reorganization and front/back-end options (snapshots, forced timestep) • Incorporate new mesh types/BC