Spacecraft Self-Contamination Computation Using Adaptive Numerical Solvers
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Solution Overview
Problem
Existing analytical models for computing self-contamination processes in spacecraft require long computing times and produce numerical errors, especially at short time scales, due to the diverse materials used in modern spacecraft, which can lead to adverse changes in surface characteristics critical for space missions.
Innovation Solution
A novel algorithm using a linear, inhomogeneous system of differential equations with time-dependent coefficients is proposed, along with a numerical solver that applies adaptive stepsize control based on accuracy requirements, allowing for the theta-method and higher-order methods like the trapezium method to minimize computing time and increase accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If numerical methods are used to compute self-contamination processes with diverse materials, then accuracy is improved, but computing time increases significantly
Solution Approach 1:
The patent transforms the original non-linear differential equations with time-dependent coefficients into a linear system by changing parameters through logarithmic transformation of the contamination flux. This allows the use of efficient linear numerical solvers while maintaining accuracy for diverse materials with different outgassing rates and time scales.
Solution Approach 2:
The patent replaces complex numerical integration methods with an analytical solution approach for the transformed linear equations. By substituting the mechanical numerical integration process with a closed-form analytical solution, computing time is dramatically reduced while preserving computation accuracy.
2Loss of time
If analytical models are used to compute self-contamination processes, then computing time is reduced, but numerical errors increase particularly at short time scales
Solution Approach 1:
The patent applies parameter transformation to convert the original equations into a form where analytical solutions remain valid and accurate across all time scales. The logarithmic transformation of flux parameters and redefinition of time-dependent coefficients enables the analytical model to accurately capture short-time-scale behavior without numerical errors.
3Ease of manufacture
If fixed stepsize methods are used for numerical solving, then implementation is simplified, but accuracy cannot be controlled and computing time increases
Solution Approach 1:
The patent introduces adaptive stepsize control that dynamically adjusts the integration step size based on the local solution behavior and prescribed accuracy requirements. The solver automatically refines steps in regions with rapid changes (short time scales) and coarsens steps in stable regions, optimizing both accuracy and computing time without complex implementation.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The method significantly reduces computation time while ensuring accuracy, enabling efficient calculation of self-contamination processes in spacecraft, which can be implemented in software tools for spacecraft simulations and computations, maintaining precise results within specified accuracy requirements.
Implementation Method 1
Self-contamination processes of a spacecraft such as a satellite may be caused by molecules, which outgas from surfaces of the spacecraft in vacuum
Implementation Method 2
molecules, which outgas from surfaces of the spacecraft in vacuum, particularly from coatings, and are desorbed from the surfaces
Implementation Method 3
A numerical solver is proposed, which applies an adaptive stepsize control based on preset accuracy requirements of the computation to minimize the computing times
Implementation Method 4
The proposed numerical solver can particularly use the theta-method, which allows solving the basic equation for deposit for time-dependent material parameters
Implementation Method 5
The proposed solver can additionally use a higher order method e.g. the trapezium method to increase accuracy
Data Source
AI summary
A method for computing self-contamination processes of a spacecraft by means of a data processing device comprising the following steps: receiving a first set of input parameters comprising general definitions of the spacecraft, receiving a second set of input parameters comprising control parameters for the spacecraft orbital data, physics, numeric, and a predetermined accuracy requirement of the computation, computing a self-contamination process of the spacecraft based on the received first and second sets of input data by either evaluating the analytical solution of a basic equation of emission or numerically solving the basic equation of emission for calculating a deposit of molecules outgassed from surfaces of the spacecraft with a numerical solver with the data processing device, wherein the numerical solver applies an adaptive stepsize control based on the preset accuracy requirement of the computation, and outputting the calculated deposit.