Adaptive Stepsize Control in Implicit Runge-Kutta Methods for Reservoir Simulation
نویسندگان
چکیده
This paper concerns predictive stepsize control applied to high order methods for temporal discretization in reservoir simulation. The family of Runge-Kutta methods is presented and in particular the explicit singly diagonally implicit Runge-Kutta (ESDIRK) methods are described. A predictive stepsize adjustment rule based on error estimates and convergence control of the integrated iterative solver is presented. We try to improve the predictive stepsize control by smoothing the stepsize sequence through combining the control of error with the control of convergence.
منابع مشابه
A Meta - algorithm to Symmetrize Any One - step Time - integration Scheme
In this paper we present a meta-algorithm which can symmetrize any one-step timeintegration scheme. The meta-algorithm creates time symmetry, even for those algorithms which are intrinsically non-symmetric. We also present the way to use an adaptive stepsize control with this meta-algorithm. It is shown that the adaptive stepsize control can be implemented naturally and easily. We demonstrate h...
متن کاملEmbedded implicit Runge-Kutta Nyström method for solving second-order differential equations
An embedded diagonally implicit Range-Kutta Nystrom (RKN) method is constructed for the integration of initial value problems for second order ordinary differential equations possessing oscillatory solutions. This embedded method is derived using a three stage diagonally implicit Runge-Kutta Nystrom method of order four within which a third order three stage diagonally implicit Runge-Kutta Nyst...
متن کاملAdaptive-Step-Size Numerical Methods in Rewriting-Logic-Based Formal Analysis of Interacting Hybrid Systems
This paper focuses on the formal modeling, simulation, and analysis of interacting hybrid systems that influence each other’s continuous behaviors. We define in the rewriting-logic-based Real-Time Maude tool a method for the numerical approximation of the continuous dynamics specified by ordinary differential equations. We adapt the Runge-Kutta-Fehlberg 4/5 method to define an adaptive-step-siz...
متن کاملEmbedded Runge-Kutta scheme for step-size control in the interaction picture method
When solving certain evolution type PDE such as the Schrödinger equation, the Interaction Picture method is a valuable alternative to Split-Step methods. The Interaction Picture method has good computational features when used together with the standard 4th order Runge-Kutta scheme (giving rise to the RK4-IP method). In this paper we present an embedded Runge-Kutta scheme with orders 3 and 4wit...
متن کاملParallel iteration of high-order Runge-Kutta methods with stepsize control
This paper investigates iterated Runge-Kutta methods of high order designed in such a way that the right-hand side evaluations can be computed in parallel. Using stepsize control based on embedded formulas a highly efficient code is developed. On parallel computers, the 8th-order mode of this code is more efficient than the DOPR18 implementation of the formulas of Prince and Dormand. The lOth-o...
متن کامل