## Conservative Finite-Difference Methods on General GridsThis new book deals with the construction of finite-difference (FD) algorithms for three main types of equations: elliptic equations, heat equations, and gas dynamic equations in Lagrangian form. These methods can be applied to domains of arbitrary shapes. The construction of FD algorithms for all types of equations is done on the basis of the support-operators method (SOM). This method constructs the FD analogs of main invariant differential operators of first order such as the divergence, the gradient, and the curl. This book is unique because it is the first book not in Russian to present the support-operators ideas. Conservative Finite-Difference Methods on General Grids is completely self-contained, presenting all the background material necessary for understanding. The book provides the tools needed by scientists and engineers to solve a wide range of practical engineering problems. An abundance of tables and graphs support and explain methods. The book details all algorithms needed for implementation. A 3.5" IBM compatible computer diskette with the main algorithms in FORTRAN accompanies text for easy use. |

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### Contents

Introduction | 1 |

Linear Algebraic Equations | 37 |

Method of SupportOperators | 47 |

The Elliptic Equations | 65 |

and Nodal Discretisation of Vector Functions | 127 |

The Heat Equation | 149 |

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### Common terms and phrases

adiabat algorithm analog of operator approximation artificial viscosity boundary value problem cell-valued discretisation chapter computes values conservation laws Const coordinates density derivative determines the analytical difference analog difference equations difference scheme differential operators Dirichlet boundary conditions discontinuity discrete analog discrete operators discretisation of scalar div and grad domain elliptic equations elliptic operator equal to zero exact solution example explicit finite finite-difference analogs first-order formula Fortran function which determines gas dynamics equations Gauss-Seidel method given grid functions heat equation implicit finite-difference scheme implicit scheme inner product iteration method Let us consider matrix nodal discretisation non-uniform grid norm operator DIV operator GRAD original differential equation parameters presented in Figure pressure prime operator properties real function right-hand side Robin boundary conditions scalar functions smooth grid space stencil subroutine which computes support-operators method system of linear test problem tions truncation error variables vector functions velocity viscosity volume