C++ program that demonstrates virtual functions, polymorphism, abstract classes, and dynamic casting in the context of differential equation solvers and computational fluid dynamics simulations. Here's the implementation:
algorithm, auto, class, command_line_arguments, destructor, constructor, dynamic_cast, iostream, memory, namespace, override, range-based, std::cin, std::cout, std::cerr, subclass, vector, virtual, void
#include <iostream>
#include <vector>
#include <memory>
// Abstract base class for differential equation solvers
class DifferentialEquationSolver {
public:
virtual ~DifferentialEquationSolver() = default;
virtual void solve() = 0; // Pure virtual function
virtual void initialize() { std::cout << "Initializing solver\n"; }
};
// Derived class for Euler method
class EulerSolver : public DifferentialEquationSolver {
public:
void solve() override {
std::cout << "Solving using Euler method\n";
}
};
// Derived class for Runge-Kutta method
class RungeKuttaSolver : public DifferentialEquationSolver {
public:
void solve() override {
std::cout << "Solving using Runge-Kutta method\n";
}
};
// Abstract base class for boundary conditions
class BoundaryCondition {
public:
virtual ~BoundaryCondition() = default;
virtual void apply() = 0; // Pure virtual function
};
// Derived class for Dirichlet boundary condition
class DirichletBoundaryCondition : public BoundaryCondition {
public:
void apply() override {
std::cout << "Applying Dirichlet boundary condition\n";
}
};
// Derived class for Neumann boundary condition
class NeumannBoundaryCondition : public BoundaryCondition {
public:
void apply() override {
std::cout << "Applying Neumann boundary condition\n";
}
};
// Base Solver class with adaptive time-stepping capability
class Solver {
public:
virtual ~Solver() = default;
virtual void solve() = 0;
};
// Derived AdaptiveSolver class
class AdaptiveSolver : public Solver {
public:
void solve() override {
std::cout << "Solving with adaptive time-stepping\n";
}
void adjustTimeStep() {
std::cout << "Adjusting time step\n";
}
};
// Function to demonstrate polymorphism
void solveProblem(DifferentialEquationSolver& solver) {
solver.initialize();
solver.solve();
}
int main() {
// Demonstrate virtual functions and polymorphism
std::cout << "Demonstrating virtual functions and polymorphism:\n";
EulerSolver eulerSolver;
RungeKuttaSolver rkSolver;
solveProblem(eulerSolver);
solveProblem(rkSolver);
// Demonstrate abstract class usage
std::cout << "\nDemonstrating abstract class usage:\n";
std::vector<std::unique_ptr<BoundaryCondition>> boundaryConditions;
boundaryConditions.push_back(std::make_unique<DirichletBoundaryCondition>());
boundaryConditions.push_back(std::make_unique<NeumannBoundaryCondition>());
for (const auto& bc : boundaryConditions) {
bc->apply();
}
// Demonstrate dynamic_cast
std::cout << "\nDemonstrating dynamic_cast:\n";
std::vector<std::unique_ptr<Solver>> solvers;
solvers.push_back(std::make_unique<AdaptiveSolver>());
solvers.push_back(std::make_unique<Solver>());
for (const auto& solver : solvers) {
solver->solve();
// Try to cast to AdaptiveSolver
if (auto adaptiveSolver = dynamic_cast<AdaptiveSolver*>(solver.get())) {
std::cout << "This is an AdaptiveSolver. ";
adaptiveSolver->adjustTimeStep();
} else {
std::cout << "This is not an AdaptiveSolver.\n";
}
}
return 0;
}
This code demonstrates the requested concepts:
DifferentialEquationSolver
base class has a virtual destructor and a pure virtual solve()
function.EulerSolver
and RungeKuttaSolver
derive from DifferentialEquationSolver
and override the solve()
function.The solveProblem()
function demonstrates polymorphism by accepting any DifferentialEquationSolver
object.
Abstract Class:
BoundaryCondition
is an abstract base class with a pure virtual apply()
function.DirichletBoundaryCondition
and NeumannBoundaryCondition
are concrete implementations of BoundaryCondition
.
Dynamic Cast:
Solver
base class and AdaptiveSolver
derived class are used to demonstrate dynamic_cast
.dynamic_cast
to safely check if a Solver
pointer can be cast to an AdaptiveSolver
pointer, allowing us to call the adjustTimeStep()
method only on AdaptiveSolver
instances.This code provides a framework for implementing different numerical methods for solving differential equations, handling various boundary conditions in CFD simulations, and safely working with a hierarchy of solver types. It demonstrates key C++ features useful in scientific computing and numerical simulations.